I doubt that thermal contraction of the engine is causing the clicks. the car cools slowly after you turn off the engine. That thing is heat soaked and takes more than a few minutes to have appreciable thermal contraction.
I expect this to be electronic based, most likely a relay controlled by a thermostat, possibly the engine fan circuit. When thermostats get close to their specified temperature, they can ping pong on/off until they pass thru fully to either off or on. I suspect the clicking is the relay reacting to this ping pong effect.
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