I've connected my multimeter in and the current draw is hovering around 3.7A with the LEDs on full power.

Just to clarify, I meant the metal casing around the rectifier itself. I haven't attached anything else to it that could act as a heatsink.

I haven't got a schematic available but it's a simple circuit. The rectifier feeds into 2 capacitors in parallel (2200uF) then through some transistors into the LEDs. There is a WS2801 chip with it's own 100nF ceramic cap for each LED but these chips draw very little current. The 3.7A I measured was taken from the output of the rectifier and represents the total load of the entire circuit.