Hi asfagus, As mentioned in your post that temps are normal for your card and this is new build so dust will be not the issue (I suppose!).
1. Which PSU are you using for the card?
2. Uninstall the drivers
, User "DriverSweeper" to remove all the bits of the old driver
and install 13.4 (most stable for me) for the GPU and then check if the freeze is there.
3. Are you using multiple RAM sticks or just one 4GB dimm? If multiple, then try to run on single stick and check. If not run "memtest" overnight to check for any errors on the memory.
Keep us posted.