How long at a time will it be switched on for? If it is seconds at a time and not too many times an hour then you'd be able to get away with 1.4A.
If it is going to be on for tens of minutes at a time I'd reckon 700-800mA would be wiser. A large chunk of the densest metal with the highest specific heat capacity you can get for a sane price (Last time I looked, osmium cost more than platinum) will help but think in terms of duty cycle.