Flippy trippy, brah!

Why do you choose the current based equation vs. the voltage based equation to calculate the max power?

Another thing to keep in mind, a fuse won't run at 100% capacity indefinitely.
If you run 2A of current through a 2A fuse, it will blow. A slow-blow fuse will last longer than
a fast blow.

Did I understand that you have the lamp dimmer on the input side of the transformer?
If it is the kind of dimmer that chops up the waveform, that will cause the transformer
to be less efficient. (i.e. it will overheat faster) Transformers Wefer a nice clean sine wave.

You could try moving the dimmer to the output side of the transformer. As mentioned, it may or may
not work at the reduced supply voltage.

An alternative would be to wire a lightbulb socket in series with your load. By putting different size
lightbulbs (25w, 50W, 75W, 100W, etc...) in there you can vary the resistance.

In that case, because we had current to work with. We knew the limit of the fuse (2A), we knew the resistance (2 ohms) and we wanted to know the power we could deliver to the load with that current.

We can flip it over and calculate the theoretical maximum power that your 12V supply can deliver with the other equation- 72W. Okay, great, that'll certainly get things hot enough, but does it exceed the current limit of the supply? Easily figured out if we use the P = I*V equation. 72W = 12V * I => I = 6A. Hmmm, not going to fly with a 2A fuse and, although it might work briefly with a 2A limit transformer, it will probably end in tears eventually.

It turns out RS has a 12V/3A transformer which in hind sight would probably have been a better replacement for the original.

But now I'm just excited to see what you have in mind with the power fet.