I suggest you use a logic-level MOSFET, but put a resistor of about 5 ohms in series with the Source of the MOSFET. That will limit the current to around 300mA, depending on the gate threshold voltage of the MOSFET, and the gate voltage that you are supplying. It will limit the dissipation in the MOSFET to around 10 W. That could still be too much and a MOSFET with thermal protection such as the NIF5002 could be a good idea in conjunction with a current limit resistor.