I am modifying a small cooler (mini fridge) that uses a Peltier cell. The cold side of the Peltier cell is in contact with the inside surface of the mini fridge. My question is: will gluing (with thermal paste) a heatsink on the mini fridge internal surface increase the cooling power of the mini fridge? Thanks
Power is a difficult word here. A heatsink will not directly change the amount of thermal energy the peltier device can transport (from hot to cold side). It will, however, enhance the distribution of the thermal energy (i.e. cooling) in the fridge. Therefore, a controller (if the fridge has one) will be able to more often use the most efficient operating point of the peltier device and thus reduce the time to (re)reach the desired temperature. But wether you actually notice an effect depends a) on the isolation of the fridge and b) on wether temperature distribution inside the fridge matters to you.
My recommendation: Try it. Nothing bad can happen and you might see an effect.
Most peltier-elements that I have seen, have a rated max difference between the hot and the cold side. I've seen alot in the ~70-100W range rated around ~70 degrees Celcius.
That means the cold side will be ~60-70 degrees colder than the warm side - so the cooler you can keep the warm side, the colder you'll get :)
Simplified example: Hot side is kept at approximately 60 degrees => cold side can get down to 0 to -10 degrees C (depending on the rated temperature-delta).
If adding a heat sink or a fan increases total heat dissipation, it should help cool down the fridge :)
Just saw that you wanted to put the heatsink INSIDE the cooler - that most likely won't do anything. You need to lower the temperature of the hot side of the peltier in order to lower the cool side as well.
If it were that easy, the fridge mfr would have already done it. As mentioned, the heat sink size is selected based on a delicate balance of cooling effectiveness when on vs heat transfer when off. Increasing in on the cold side would just mean that when off, the sink will conduct heat back into the fridge faster. So ultimately it results in your Peltier element running more often to get the same net effect and may actually WASTE energy.