If your PSU fan is not working at all, that certainly will reduce the cooling of your case and cause higher temperatures. How much higher? Depends on how many other fans your case has. But you still need a cooling fan operating inside the PSU to keep it cool at least.
The most likely cause is that the fan inside the PSU has failed. You have two choices. The easy (but more expensive) option is to replace the entire PSU.
If you are good at fixing things you can replace the fan only. Most PSU's use very common computer case fans, like a standard 80mm style, so they are not hard to find. To do this you would disconnect the PSU completely and remove it from the case, as if you were going to replace it anyway. You will need to remove screws to open the PSU case itself, and possibly break a seal that warns you that you may invalidate its warranty. Once you remove the cover, BE VERY CAREFUL poking around inside! These units have large capacitors that may still have a charge stored in them enough to shock you. Try gently moving the fan blades with a stick or screwdriver. They should turn very easily and keep turning for a bit. If they are stiff or seized, the fan bearings are worn out. Examine the fan. It is probably mounted into the PSU with 4 screws that can be removed. As you do that and lift the fan out, look very carefully at the outside of its case. Usually there are two arrows molded into the plastic. One points around the fan to indicate the normal direction of blade rotation. Another points to one side of the fan to indicate the normal direction of air blowing. Make sure the replacement is mounted in the same way.
Once you have the old fan out (even if it is not disconnected yet - see below) you can see what size it is. If you are not sure, complete the disconnection step and take the fan with you to a computer parts shop to get a replacement.
The fan's power wires MAY be soldered into the PSU printed circuit board, or they MAY have a plug-in connector on their end. So you may have to do some soldering work to disconnect the old one and replace it. I did this job recently, and I had to use a small soldering iron to splice the new fan's wires to the snipped-off end for the old ones, using heat-shrink tubing to insulate the soldered connections, but electrical tape can do that job, too.
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