Do tire temperatures affect whether a car is oversteering or understeering?

Is there a connection between a Formula 1 racing car's tendency to oversteer or understeer to what the temperatures are? Is it safe to say that an understeering car will heat tires more?

In principle yes. If the front tires are very cold, then the car an understeer because of that. If the car in general understeers a lot it will put more stress on the front tires and they will wear out faster.