What do they use for radiation shielding for circuitry? Lead?
Nope, that would be too heavy. The key to radiation hardening is to use larger process sizes. Although it makes your transistors bigger and therefore increasing the chance of a particle hit, it decreases the effective amount of charge that particle can dump into the silicon comprising your transistor, thus reducing the chance of a bit flip. Basically, the smaller your components, the more vulnerable they are to the damaging effects of ionization. The second thing you need to do is harden the chip circuitry itself, eg putting ECC on everything.
But anyways heat may be another concern. In a vacuum there is no air to cool a CPU, and the higher a CPU's clock rate versus a lower clock rate, the more cooling is needed for the higher clock.
Well, without air, the CPU still cools. There's thermal contact with the circuit board and furthermore, radiative heat loss. However, low power 33MHz parts don't get that warm. For devices like the Mars Rover, they actually have to put electrical heaters in the control unit to ensure it doesn't freeze, since your average Martian night is bitterly cold.