It does seem the laptop is overheating. You should check to see if any of the intakes or exhaust vents are blocked by dust build up. I assume the laptop is on a hard surface like a desk rather than on a soft surface like on the bed or chair cushion where the vents could be blocked. Laptops should never be placed on soft surfaces.
If it is in fact on a hard surface and none of the vents are blocked, then the laptop seems to have an overheating problem. It should be checked out by a laptop repair shop. Normally, I would recommend you send it back for warranty service if the warranty period is still valid, but that process can take weeks which is not good if your daughter needs the laptop for school. Bringing it to an unauthorized Asus technician for repairs will automatically void the warranty. Not a big deal if the laptop is no longer under warranty.
The issue could be the thermal paste which helps transfer heat to the heatsink and then blown out of the exhaust has "dried up". Cleaning up the old thermal paste and applying new thermal paste is fairly easy. The problem is taking the laptop apart to do what is necessary. Therefore, most of the cost will be related to labor.
The short term solution is to go into the advanced power options set the laptop to either Sleep after something like 15 / 30 minutes or whatever you / your daughter thinks is reasonable.
An additional step is to limit the clockspeed of the CPU. If the Asus has a Core i5 CPU, then it has something called Turbo Boost which automatically overclocks the CPU if it is busy and a long as it is not too hot. For example, my Core i5-2410m has a clockspeed of 2.3GHz, but with Turbo Boost it can go up to 2.9GHz. Core i7 CPUs also have Turbo Boost, but Core i3 CPUs (and below) do not have this ability
In the advanced power options you should see something like Maximum CPU Performance (or similar), expand that section. The default setting should be 100%. Reducing it to 99% will disable Turbo Boost if the CPU has that capability. Setting it below 99% should further reduce the clockspeed, however it does not work the way you think it would work.
Using my i5-2410m as an example which has a normal clock speed of 2.3GHz. Setting it the max CPU performance to 95% does not mean the CPU will then run at 2.19GHz. It seems to be setup to work in stages and will likely be different for each CPU model. I think setting the max CPU performance to between 90% - 98% will actually mean the clockspeed will be limited to 1.8GHz. Between 76% - 89% it will be 1.6GHz. You get the idea, it's not intuitive. Naturally the lower the clockspeed, the slower the laptop will perform, but it should also result in lower heat.
Last resort.... toss it out the window.