I think it is more related to the modem... ping lag means internet connection problem.. if graphic stutter or PC becomes slow then only considered PC overheat.

I think you can easily install some MSI software which help to monitor your PC temperature, in the software you can set the threshold temperature for CPU and the PC will beep if the temperature hit. The sames goes for the graphic card.

The fastest way is to run bothe cpuz and gpuz... as the forumer suggested. But I forget if the temperature is shown.

I suggest that you take a stand fan and place it next to your modem... when the ping start to become high, try turn on the fan and see if the ping goes down... such way you can know for sure weather is the modem.... and eliminate one of the factor

maximum for intel i5, I'm not too sure... 80 plus degree is quite normal.
But CPU nowadays very smart. Once you hit threshold temperature, they will throttle automatically and your CPU will not fried.
Not like last time, overclocking can easily cook the CPU

Wonder if TS solves his problems

It is normal for graphic card to be very hot during gaming... that is why it has huge heat sink spanning through out the length of card. But do mind that although you feel hot when touching the heat sink, it does not necessary mean it overheat and cause your ping to be high.

I suggest that you take a stand fan, open the casing and directly blow on it during your next gaming session. See if the ping will lag again. If it still does, then the problem is not your graphic card

Oh... in this case, you have find the root cause of your problem.
Just wondering, what is the model of your graphic card and what is the game you are playing.
Custom graphic card heat sink is not very common and usually cost a bomb, my suggestion is to save up for full upgrade loh...