I have close to 500 LEDs in a strip, each strip has sets of 3 LEDs in parallel, connected in series, with the appropriate resistor. I'm definitely hitting close to the max Amps, and yes, they're 12V LEDs.Just because a power supply is rated at 20A doesn't mean the circuit will draw that much current. I'm betting the thread starter doesn't have 20A worth of LEDs here.
Yes the transistor gets hot, but not burningly so. It's rated at 30A so I think I'm fine there.