I bought an MSI 7770 yesterday and have been having fps problems. When I start playing any game the fps always 30+. For example I play Dota 2 and all my setting is on high and fps is running smooth at 60+ fps. Then after about 5 minutes of play the frames drop to an unplayable 15-30 fps and spikes up and down. very unstable.
I have a 460W Coolermaster PSU. It seems like when a GPU overheats but it runs consistently cool throughout gameplay. I doubt that its my CPU bottlenecking it because Im running a 2nd gen i5 2400.
Download HWMonitor, run it, then run the game, and when it starts lagging, minimize the game, maximize the HWMonitor window and capture a screenshot. Upload it to www.imageshack.us (don't forget to select "Do not resize" option) and post the link to it here.
Although it is only good for 430W, that Crappermaster PSU is not their worst: http://www.hardwaresecrets.com/article/550 and a 430W PSU should be able to run a HD7770 without problems.
Your problem does look like thermal throttling, and it could be of the CPU as well. Do you have good airflow through your case? Make sure your fans aren't fighting each other so you do have flow through your case.
What graphics card did you have before? Did you clean off the old drivers before you installed the new card?
I do have sufficient airflow in my case. My case is mainly always open on one side. Previous gfx card was GTS 250 and I did uninstall all the previous drivers, installed new one. reinstalled new ones and back and worth, still no solution.