Ok. i appreciate all the help, but i have one final question about over heating.?

a while back, by alternator belt (which also turns the waterpump) broke on my way to school. i bought a new one promptly, but i couldnt put it on myslelf, so i was forced to drive the car home without it. this is the first time the car ran hot. i stopped periodicly to let it cool down, but it still ran almost in the red zone. i put the belt back on, and its still overheating. so... did i damage my engine/thermostat?