Usually discomfort means your body doesn't want any more of what it's getting.
But yeah, much like with people working (processing) harder means more heat is being generated. Of course more modern processors are more efficient and the amount of produced heat hasn't followed the near-exponential growth of processing power, but combining less ventilation with more power…
A cooling pad, as said, might help. But honestly I fear it would only slow down the buildup of heat. More time for you, sure, but just an extension. How much? I don't know, but something. I'm not an expert.
Try turning down the settings in the games, in case you haven't done so yet. Less work means less heat.