Fireplaces, Heating Stoves, Flues and Chimneys - I can't get my gas fireplace to stay burning

At first I had trouble with keeeping the pilot lit. Finally, it did, the full flame. But it seems after a half hour or so, it goes out. When I go over to turn the on/off switch 'off', it smells very hot. Much more so than it ever had. I only bought the house two months ago, no paperwork on the fireplace. Full tank of gas. Any ideas? I thought maybe something got clogged somewhere and a thermostat or something reaches a certain temp. and a safety switch or something goes into effect. Does that sound possible? Help!! I really need that heat in this large den b/c it is an addition on a concrete slab. Thanks!