OK. Some interesting and informative material being offered.
To continue, a couple of follow up points, whether it be oil or water: I'm not sure immersing a typical OEM PowerJack style torroid into either oil or water is a good idea. It was never designed for that environment (think glue, adhesive, wire coating). In theory, either distilled water or mineral oil could serve as a safe, non-conducting medium, though. Off the top of my head, I'm thinking an epoxy coating (2-3mm) should be a decent thermal conductor; so probably not a design impediment.
Then it occurred to me, why aren't we using mineral oil as a coolant in our cars. Doesn't deteriorate, no problem with metal rusting, won't freeze. Long term thermal transfer OK, short term, not so much. Given how quickly these small torroids can heat up, I would think oil is not the best choice. Just a guess, offering no proof.
I personally have no need for liquid cooling, but as to practical info on enhanced air cooling - - read on.
I've been using two PJ8000-24s (2016 version) 24/7 for the past two years where I modified the cooling via enhanced airflow.
Opened up the torroid core to let it breathe, tilted it on to its short side, added a 235 cfm fan to blow through the core in wind tunnel fashion. No need to change any wiring lengths, just some careful bending of the primary wiring. Needed to add a 2 x 18" metal piece on each side to support increasing the case height. The torroid sits on two short lengths of thick wall 1/2" id silicone tubing, currently unsecured; but gravity is my friend.
Heat be gone! This behaves like it could run for hours at 3500-4000 watts, if you've got the continuous 165A to spare from your batteries. I tried 20 minutes at 100A and was then able to grab on to the torroid and hold on for 5 seconds before having to let go. So, pretty scientific measurement . . . . .
Bought a third PJ8000-24 as a spare (late 2018, the new look case with replaceable daughter boards). They added a top mounted fan mostly centered over the torroid. Unfortunately, the torroid core is still is still blocked by the mounting solution they use. From their standpoint, its the only practical way to do it for shipping reasons.
If you need more cooling, though, it's easier to do with this new model. Just remove the mounting bolt and top/bottom core cover pieces to open up the center. To go a step farther, fashion some metal air deflectors to enhance the airflow pattern around and through the torroid. While not as effective as my wind tunnel design, I'd expect you'd see noticeable cooling improvement.
At some point I want to try supplying the inverter air input with cooled air via an evaporative pad during my hot, dry summer season. Could cool moist air be the reasonable compromise in this discussion?