Hi @robbie12
Can you hear if the fan in the laptop is operating (or feel if air is coming out of the exhaust vent, left side of laptop) when the laptop is turned on?
If not it could be a faulty fan.
If so it still could be a fan problem i.e. clogged, therefore the heat generated by the CPU is not being expelled fast enough.
Here's the ifixit Toshiba Satellite C650 Series repair guides.
The C650D and C655D-S5084 guides show how to replace the fan so that you can check if it is OK or needs cleaning. The procedure is generally the same for all C650 series models if you have a different model (see model number on product label on bottom of laptop)., although the fan model might be different, I'm not sure. If the fan is faulty look for the fan make and model number which is usually on the fan itself and search online using that information to source a correct replacement.
Since you have the laptop open to check the fan, it may be worthwhile to refresh the thermal paste on the CPU and GPU on the motherboard because after some time it dries out and becomes less effective in helping to transfer the heat from the CPU and GPU to the heat sink so it can then be expelled by the fan.
Here's a video that shows what to do in a C650 series laptop. The CPU and GPU can be seen from about 6:00 minutes into the video.
Here's the ifixit 서멀 페이스트 도포 방법 guide that may also help.
3 
1 
1.6k 