Calculating MOSFET Power Dissipation

Hello all,

Let me start this post by saying I've read the sidebar and scanned the wiki for relevant information before posting this.

I'm planning to build a 9x9x9 RGB LED cube as a class project, and need help figuring out if a MOSFET used for switching power to the LEDs will need a heatsink. The case will have active cooling (a few 40 or 60mm fans), and I can place the heatsink directly next to airflow if needed.

The grid of LEDs will be powered by a 120VAC -> 5V 60A switching power supply (as the cube can draw 9^(3)*0.06 = 43.74A in the worst case). I'll run the output of this supply to the drain of the MOSFET and the source pin will be wired to the +5V pins of the array of LEDs, with the gate pin controlled by my Raspberry Pi (with a voltage booster if necessary).

Using the 43.74A figure and the datasheet for a MOSFET I'm looking at, it seems like the power dissipation range (I^(2)R using R_DS at 25°C and the maximum rating of 150°C) will be 16.07-23.72W

This is where I get stuck. I know that I need to factor in the thermal resistances for channel-to-case, case to heatsink (is this equal to the thermal compound's resistance?), and the heatsink, but I don't know how to apply these values.