There is a gas in the fridge R134a , freon or something. When compressed it turns into a liquid and gets hot , the heat from this is dumped ( normally out the back ) via along thin metal cooling coil.
When the compressed liquid is de-compressed it goes through change state cooling and goes cold. The cold liquid runs around inside your fridge , making it cold. There is a small orofice valve that lets the liquid through slowly and lets it expand.
This is a very basic description of a fridge.
No the sides should not be hot, but the back should be.
Maybe pull the fridge forward and remove all the dust thats on the coil