Heating Problem: Powering Arduino Mega 2560 with 5V - 10A Transformer

What is over-heating, the transformer or the arduino

I take it your "transformer" provides a smoothed DC output and not AC as a transformer does.

6 x 10*-3 x 100 = 0.6A not 6A as you show.

Can you supply a diagram of how you have connected things up.