Anything under 250°F or so is great. It also depends on the type of diff and how hard you're driving it.
Back in my racing days, we logged or even had live telemetry for diff lube temp. With certain types of limited slip units, that's one of the fastest responding readings to track conditions. We could literally see the car going through corners and down the straights by the changes in the diff lube temp. The temperature would spike quickly in the turns, and it would cool slowly but significantly on the straights. On a high powered GT car I worked on, we saw between 220°F and 300°F at different parts of the track. Ours had a cooler for the diff lube with a thermostatic fan that cut on at 240°F IIRC. And with the design of the diff we had, with the drain plug lined up with the ring gear and getting a lot of movement in the lube at the drain plug, we didn't use a pump. Our gears would pump the lube through the cooler loop. The drain plug was plumbed to feed the cooler, and the fill plug was plumbed for the return.