Sounds a little low for the thermostat to open, high 80s to low 90s would be more like it...
The best way to check it though is to remove it and boil it in a pan and check what temp it opens at, you can't really trust just the rad being warm as an indication of the thermostat being open or closed as a lot of cars allow a little water to bypass the stat before it opens.
That said, if your going to go to the trouble of removing it you may as well just fit a new one anyhow as they only cost a few quid.