I don't see any good reason for the answer not to be "indefinitely".
The CPU and GPU come with fans that cool those parts down.
It may not be the most effective way to cool them down, but it will do so at least reasonably well.
Cheaper video cars and standard processor fans tend to use a dispersal method of part cooling. This means that a fan blows directly on the hot part continually and that the hot air is continually pushed to the side of it but the hot air does remain in the case afterwards.
This is why cases have fans that suck air in (generally from the front of the case on the bottom) and they have other fans that suck air out of the case (generally on the back and on the top).
This setup ensures that there is new cold air to blow on the hot parts continually and (since heat rises) there is a way to continually get hot air out of the case so thermal temperatures cannot rise beyond a certain threshold.
Some of the more expensive video cards and processor coolers actually aim their fans so the hot air doesn't get dispersed inside the case, but it actually blows air from the front, over the hot part, and straight out the back. This ensures that the hot air from these parts exits the case immediately. This is a better overall system, but a more expensive one as well.
Those sorts of things are luxuries that budget conscious people don't usually end up getting their hands on.
The budget conscious people fall back much more heavily on their case's airflow to get rid of dispersed heat.
Luckily for you, the 300 Illusion case is well equipped for this sort of application.
The 300 illusion brings twice as much air in and pushes twice as much air out as cases the average computer user tends to have in their possession (like the first cheapy one I had to go with to get under the budget).
Twice as much cold air in and twice as much hot air out will go a long way toward making sure that the components cannot get into a viscous upward cycle in internal temperatures.
This avoids the cascade problem where a device gets hot, the air around it gets hotter, because of that the device itself gets hotter, which again causes the air around itself to get hotter, and so on.
A good cooling situation will reach an equilibrium temperature at which the temperatures remain constantly stable.
How expensive the case is and how well it is designed will dictate where that equillibrium temperature lies in the thermal spectrum, but even though cases can go into the $300s alone, the regular $70 cases like the 300 Illusion that I chose will still be able to keep temperatures stable (although at a higher temperature rating).
Pretend for a moment that a video card could get up to 100c in temperature before it would cause the system to fail.
A normal dispersal fan would be able to perhaps keep the part down to about 60c if the video card was just hanging off in the air somewhere with the ideal amount of air that it could suck in and the ideal capacity for air to be removed from the equation by just floating up into the sky.
If you put a regular case on it with poor airflow (no fans in passive intake, 1 fan out active exhaust) then the video card might find an equilibrium temperature of about 90c.
It is pretty close to failure, but not quite there, so even then this case should perform decently. However, if the passive air intake on the front gets clogged with dust and air intake is obstructed, that would potentially cause the temperatures to increase and cause the video card to fail.
If you, however, had a 300 illusion case or something (2 active intake fans, 2 active exhaust fans), then the equillibrium temperature for the video card might equalize at perhaps 70c. There would be less chance of clogging the active intakes and they would probably have filters that you can clean fairly easily to prevent these sorts of problems.
If a clogged filter caused the temperatures to rise 20c, you would still only be at 90c total so it would take a lot of neglect for the temperatures to rise into the dangerous territory range.
A $300 case with like 5 active intake and 5 active exhaust fans, however, might be able to give the video card essentially the perfect environment (as if the video card were hanging off in the air) where temperatures stabilize at the lowest possible air cooled temperature (the 60c basic temperature that the dispersal fan can produce) and it may take so long of neglect to completely clog the intakes as to make a scenario that allows for +40c internal have a likelihood of something south of 1% in almost all realistic environments.
Such a case would likely cause the video card never to break 80c, much less to start approaching 100c.
There are crazy expensive frozen helium cooling systems that could be attached instead of a dispersal fan onto the video card processor that can keep the thing down to like 20c as well, but those are the sorts of luxuries I talked about before that budget builders don't usually get their hands on.
In any event, if the case is constructed according to the documents, all the fans are functional, and so on, there is no good reason that any device should be remotely close to the temperatures where failing becomes a real possibility.
Just make sure to clean the filters once a year or something (unless you are in a particularly hazardous environment or something, which would mean you need to do so more often but you should still be fine).
I don't think that you need to really worry about additional cooling other than what I factored in above with the case and so on.
The people who need to worry about this are generally the people who are trying to push their cards to the maximum limit.
Whereas your CPU might be kept at a reasonable 60c with a stock fan, it is possible to make it work maybe 20% harder and to have it generate maybe 40% more heat. The dispersal fan wouldn't be able to keep this at 60c anymore. It might not be able to keep it under 90c. This sort of scenario would mean you definitely DO need a better cooling setup in order to keep the processor out of the danger zone.
Unless you see that situation occurring with your parts, you don't need to worry too much about it.
Before you undertake anything like that, I would use it a lot in the standard configuration first just to get a handle on things.
A program like HWMonitor from CPUID can tell you (for free) the temperatures inside your case so you can monitor them and compare them to the maximums you want to achieve.
Anyway, long story short, I don't think it is something to worry about at this moment.
However, I did neglect to mention one key point that may or may not need to be mentioned.
There absolutely must be thermal paste between the processor and the processor heat sink (what the processor fan blows air across). If there is not any, the computer will not stay on for more than about 3 seconds because the heat sink won't be able to take heat away from the processor itself and the processor fan will be blowing air on a cold heat sink and it will have no way of applying air to the hot part (the heat sink would be "in the way").
Thermal paste allows for heat to be moved from the processor chip onto the fat metal heat sink fins where the processor fan can blow air across it so the system will be functional.
Thermal paste may or may not be included with the processor. I don't know that specifically. If it isn't, you will have to buy some of this to put on it. It is very cheap, though, at like $5, so it shouldn't be a very big deal.
Even if you had some sort of aftermarket cooler that costed like $50 more, it may not come with this $5 paste and you might still have to buy it separately.
Anyway, just get the same things as listed and if it doesn't come with paste in it then pay the $5 or whatever for a squeeze tube with this stuff in it and use it.
You can get some ahead of time if you want from a regular computer parts store I think or by ordering it off the internet somewhere.
Anyway, if you still have questions ask away.
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