Especially a good idea to rebuild the lower end since coolant + oil wreaks havoc on bearings.
I had my alt/water pump belt snap off a few months ago. Had to drive it about 2 miles to a shop like that, eyeballing the temp gauge the entire time. Thing is, without the pump flowing coolant through the block I'm not certain how accurate the gauge was. I made myself park the car whenever the gauge hit medium and let it sit (it was 0 degrees out, so that helped).
I'm super paranoid about running any car hot. My first tuner car (Mitsubishi Starion) warped or cracked the head super easily whenever it got hot