Transformer has a 550mA rating, appliance is 3A - I guess it wont work very well?

I really dont mean to sound so stupid but can someone confirm b4 I condem a second very cheap transformer to an instant death. - Appliance is a 12V (rated 3A nominal, but no rating for watts given) car cool box I'd like to run through the mains. obviously I saw the correct adapter in motorworld for 14.99, but thought ' hey they're only 3.49 in poundstretcher next door...' (and the cheap ones are so small and neat compared to that big one with all those fins on). I guess I'm answering my own question here, but the opinion of someone who actually knew would be great