Electric wires and outlets are sized and rated by wattage and load delivered to the plugged in appliance. I suspect several things that may affect your hot electric outlets.
First, use a space heater sized small enough to operate safeley where it is plugged in to the wall. Most outlets in family rooms and bedrooms are rated for 15 amp loads which can deliver 1800 watts of heat. Be aware that other appliances use part of that wattage capacity so the space heater is just part of the load on that circuit.
Second could be a loose wire in the plug outlet in the wall so have your outlets and wiring checked by an electrician for safe operation.
Third could be a possibility of aluminum wiring in your home. Aluminum wiring has been the cause of some house fires due to hot outlets like you describe. This outlet problem can be solved by an electrician checking or replacing your outlets with devices approved for aluminum wiring. Your electrician holds the answer.