You need to clarify a bit more. It all depends on your current configuration and the resolutions of your monitor and HDTV (screen size does not matter).
If your GPU were plugged into both a monitor and HDTV and used at the same time, then yes, it would put more stress on the GPU (but it is designed to handle that).
If you were to connect your GPU only to your HDTV and the HDTV has a higher resolution than your monitor, then yes, it would put more stress on the GPU. If the HDTV and the monitor have the same resolution, then it wouldn't cause any more stress than the GPU already experiences when connected to the monitor.
The inches dimension of the tv is immaterial to the graphics card. It is the resolution that matters. If your TV is 1080P(1920 x 1080) then it looks the same to the graphics card regardless if it is 32" 24" or 60" or a 1080P monitor.
Plus, you'll be fine!......go ahead and plug into the TV. It's max res won't be higher than 1080p (unless you're an early adopter of the new 4K tv's, and loaded!)
The worst you may need to do is lower the res or eye candy of some of your games, however, (providing you have an HD tv) you will be able to view any HD content you have on your pc. But yes, we need more info as was said above.