Andrew Burgess wrote:
On the adaptor it will say something like input: 120v ac, output 9v dc 500
mA. In this case you're looking for something that has an output of 12v dc
and 1000 mA, which will give you a slightly dimmer bulb, but a longer bulb
lifespan.

Yes ...if you want the full Wattage from the bulb then
ex: 12 volt bulb at 20 watts 20W/12V= 1.67 Amps is the minimum
transformer you will need but as you said if you want lower brightness
then you can go lower as you please.

This will overload the transformer and it will get hot.

If a transformer is rated for a certain current then it can take this
current. It is when you go over the rated current that a transformer
gets too hot (they all get a little warm).