It's possible to build a thermometer out of a bimetallic strip by rolling it up into a spring shape. As the temperature changes, the coil unwinds.
Therefore, we should take a large sheet of plutonium, and bond it to a large sheet of uranium, and roll it up into a deliciously radioactive swiss roll.
The swiss roll will then be dunked in a nice cup of liquid moderator. If the temperature changes, the geometry of the roll changes in step, and the ratio of moderator to fuel will adjust, changing the speed of the reaction.
Some careful engineering will be required to get the numbers right, but it should be possible to arrange things so that we end up with a completely automatic, constant-temperature reactor.