Burning a Power MOSFET
Per datasheet, maximum junction temperature is 175C. (Tj max)

Per datasheet, thermal resistance, junction to case is 0.18 K/W. (Rthjc)

You would like to dissipate up to around 370W, I guess. That must be a decent high-discharge cell to put out that much power. Let's just round it up to 400W.

So the maximum case temperature you can allow is:


175 - 0.18 * 400 = 103 C


You need a heatsink and fan combo that can dissipate 400W while keeping the case under roughly 100 C. Let's say ambient temperature is 40C. So your heatsink rating must be:


(100 C-40 C) / 400 W = 0.15 K/W


So you are looking for a heatsink or heatsink and fan combo that can maintain that thermal performance (lower is better). Note that the unit C/W and K/W are the same thing when evaluating heatsink performance.

I think it may turn out to be impossible. After a quick look, the only thing I found was liquid cooled heatsinks that have 0.43 C/W thermal resistance. But you can look some more and see what turns up.

Generally, it will be cheaper to dissipate power in resistors than transistors, and power resistors are available that can operate continuously with surface temperatures far above 100C, so cooling is often much simpler.

Also, even though the OP said the application is within the safe operating area (SOA) I didn't see an SOA chart in the datasheet, so I am skeptical about that claim. My answer shows that this is a challenging or maybe impossible application, even if SOA is not a concern. But the SOA issue is also important.