Just to add my $.02....
I installed a diff cooler with an electric pump and electric fans during the build of my car. I also have a diff temp sensor, and the pump/fans are set to go on when diff oil temp reaches 240 F, and goes off when it's down to 220 F.
I am running an R200 short nose with Giken LSD with the Giken oil.
In street driving, even in 100 F weather, it never goes on. Diff temp stabilizes at about 210 F.
On track, with 20 minute run sessions, the diff just barely reaches 240 F at the end of the session. The system usually switches on just as I am entering the pits, cools the oil to 220 F in a minute or so, and switches off. This was the case even during a 93 F track day.
So I am wondering, for my purposes, if diff cooling is even needed. The oil would cool anyway as the car sits between track sessions. On street it's a complete non-issue. The Giken people said their diff oil is fine up to about 270 F. Obviously it would be needed for endurance racing or long track sessions, but neither is me.
So I read all the machinations here about diff coolers, and thought I should mention that I am considering removing mine, just in the interests of simplicity and lighter weight. The pump, cooler, mounts and plumbing probably weigh 5-10 lbs.