TL😀R probably not the GPU causing frame rate loss, and if it is then heat probably isnt the issue.
Not an expert here, but I have basically the same card, MSI GT 710 2G3D LP. I don't play GTAV on it, but everything I read says that game lags easily based as much on your CPU, RAM and HDD, so GPU shouldn't be as big an issue unless its to close to max overclock which will cause stability issues differently on different games. If your overclocking the GPU, back it off a little and see if that helps. I can play Just Cause 3 on all low settings and 800X600 resolution if I overclock the card to 1250MHz and juice the VRAM +200MHZ and it gives me near 30FPS and stays under 60C. If I raise the settings nay higher, it gets real hot and real laggy. I don't think the GPU is your issue, maybe do some system cleanup, check any autorun programs you don't need running, make sure your other hardware is up to par for the game and if all else fails, try adding RAM if you aren't already far over the minimum spec. Also, my card suffers residual heat from my CPU so use CPU-Z to check other temps, it may even be your CPU thats lagging AND adding heat to the graphics card as well.