although your description of the events is somewhat nebulous. it seems to me that it could only be a few things
1. thermostat stuck closed (coolant temp will not be hot)
2. coolant leak (you would probably notice that straight away)
3. your cooing fan is not coming on when coolant temperature rises.
if #3 is the problem you could find out if the wiring, fusue, or the sending unit is intact, and functioning.
you could also hot wire the fan to come on at all times, or perhaps when you turn your parking lights on