If it gets really hot, the humidity from bedding(shavings) will cause respiratory issues which can lead to death. I personally switch to pellet bedding in summer months to help avoid this. This is one of the many reasons I frown on the "big tub" caging so many people seem so happy with.
and I do agree, 70-80 is an optimal temp but not crucial. My rats see 90's in the summer months ( I have fans in my building) and see a low of 45 in the winter.