Using your TV as a monitor will not burn out your graphics card or cause any harm to it. You can use an adapter to hook up a VGA monitor to that card if you wish, and that also will not harm it, neither will hooking it up via HDMI to a high resolution display.
Graphics cards are typically only harmed when they run too hot, usually due to insufficient airflow in the case, poorly installed heatsink, or overclocking. Overvolting the card when overclocking can also damage them. If you are worried about temperatures, download HWMonitor and it will keep track of the temperatures of your PC's components. In any case, the temperatures should not get too high anyway outside of gaming, and even then, assuming you don't have cooling issues the card should not get hot enough to damage it.