Leaving aside the question (debated elsewhere) of whether or not you need an oil cooler, let's say you've decided you need (want) one. And you've decided to use an oil cooler thermostat so you don't have (to listen to) the common objection that the oil takes too long to heat up, or never heats up.

Instead of using one of the various aftermarket oil coolers, which are either very expensive, or require custom work to mount them, why not get a transmission oil cooler from an automatic Mini and use that? It mounts cleanly, in threaded mount holes you already have, and they cost about $260 brand new, or half that for a used one.

In a perfect world you'd put your oil cooler next to rather than in front of your water radiator, but none of the aftermarket options do that anyway, because there's no place you can do that. And it's generally understood that it doesn't have much negative effect on your water cooling anyway. Link.

Any reason not to do it that way?

 

Tranny cooler may not be able to take the pressure

 

That's definitely a good point to consider.

Just as an approximation, we know that oil cooler lines are generally low pressure -- under 100 psi, so they use ordinary spring clamps or worm clamps. The Mini oil pressure should be 25 to 80 psi at 3,000 rpm according to the Bentley manual. The oil pump bypass valve prevents the pressure from going too high. The type of hoses and clamps we see on the automatic transmission cooler appear to be of a higher grade. They are not plain hose with a removable clamp, but are pre-made with fittings permanently attached, typical of high-pressure hose, albeit they are only plastic fittings, so they aren't what you see on 2,000 to 4,000 psi hydraulic lift systems. Generally, automatic transmissions oil pressure shouldn't go above 250 psi.

So whatever it's rated at, it's quite a bit more than the engine oil pressure.

You do see a lot of hot rod parts where they use pre-made braided high pressure hoses, with aircraft grade fittings. Sneed's cooler kit has plain, low-pressure clamps or an optional hose rated at 300 psi for $200 more. I always guessed this was because high-grade hoses look cool, and perhaps racers or whomever are hoping that by overdoing it, they are getting durability. That 300 psi hose will never fail at only 80 psi, right? I hope not.

I can't find a specification for the Mini's transmission oil pressure, but I'll keep looking. It's a good thing to check.