My first guess is the antenna amplifier is on. Many power outlets get their power from the same circuit the antenna amplifier is on. Turn the amplifier is off. Many have an LED to show if they are on or not.
Otherwise, check to see what else is off when the fuse blows just to make sure something else like a fridge etc isn't drawing a bit of power from the same circuit.
Also, it may make a difference at what the setting is on the heater for temperature. The difference in the surge could be different if you turn it all of the way down, turn it on, and then gradually turn the thermostat up.