95 Wrangler, 4 cyl, 5 spd.

Knocked a hole in the radiator, so I just put in a new OEM radiator and hoses. Also, flushed out the coolant and replaced.

Before this, the temp gauge showed a steady 195-200 once she warmed up. Now, temp keeps going up to about 215, then drops to about 190, over and over. I assume the thermosat is opening and shutting repeatedly (I know I should have replaced it while I was in there).

Will this hurt anything if I don't get around to replacing the thermostat for a while? If it fails completely, is it more likely to stick open or closed?

Thanks.