The normal way laptops were designed, when included a GPU, was when in 2D applications the integrated graphics were used (Word, Excel, Websurfing) but when you need graphics ((Games Videos, maybe even your diag software) the IGF was not capable enough to run the video so the added GPU would run.
I believe, as I understand, your mainissue is heat, it may need a good dusting, but by the age of the hardware your mentioning, I believe it may be more just end of life. If you are unaware, that GPU was put on the No longer supper list, and the Core2Duo is very dated. If the hardware has been used for a very long time, it just may be at end of life, as PC parts are only guaranteed for 3 years under normal 'office' conditions (40 hours use per week).