Overheating and bad battery???

I own a 2001 Monte Carlo and it keeps overheating. I thought it was because
one of the cooling fans was faulty so I replaced the whole assembly. I had to
pull over and cool off three times on the way home from work yesterday and
the first time I pulled over and turned off the car my battery needed a jump
start and the new fans didn't activate until the third time I popped the hood
and the temperature was low the rest of the way home. I didn't even need to
jump it. It was as if there was nothing wrong at all.  Had a similar problem
last weekend. I stopped at a stop light and my car just stopped entirely. Took
two hours to jump start it again but I figured that time was because of me just
being stupid after I topped it off with coolant and forgot to put the cap back
on. What am I missing here?