you are thinking a heat sink for a computer,
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a heat sink for a bator is different, i have also seen people adding ceramic tiles
I'm thinking of a heart sink from my college physics and thermodynamics classes. What you are talking about is a thermal mass. Two different things.
There should be no reason for a thermal mass in that incubator. As long as it does not interfere with the operation of the incubator it won't hurt anything. Your homemade incubator may be different but if a thermal mass were required the incubator manufacturer would have installed one, provided one, or at least mentioned it in the instructions.
If you have regular power outages a thermal mass can be very beneficial, but with a steady power supply it's just not necessary.