One would think that a vendor of such items would have that data and use it as a selling point. Because they don't, at least I haven't seen any actual "hard data" listed, I have to believe that cooling is minimally improved, and only as a result of the following two or three possible benefits of running such a cover;
1. Most are "deeper", meaning they can carry more fluid. More fluid = extended service intervals and potentially more cooling - until it is ALL warmed up.
2. They are generally stronger than the "stamped tin" covers found on most diffs. Therefore they are less likely to be bent, or worse, punctured or crushed when struck by road debris or hanging up an a obstacle off roading.
3. Often, they run higher quality drain plugs with larger magnets that latch on to more fine metal shavings as the gears or bearing wear in. Some have lower, easier access to said plugs for ease of maintenance, for when you do service the unit.
4. Some are "Finned" like air cooled cylinder heads and MAY shed some heat with just the wind blowing on them going down the road. Though I doubt that a healthy diff would produce great enough heat to cause premature failure of any of the parts inside. Also, the added thickness of the more robust units built for intended serious off road rock crawling abuse may even serve as a bit of a heat sink just by the added wall thickness... until that all comes up to a given temp as well.
5. So, the main thing here, is that they LOOK "Cool". Sure, there is some small mechanical benefits that might be realized after MANY miles of VERY heavy towing and / or slipping of a LSD unit (if equipped). I imagine that a "healthy" unit, with good components, sufficient fluid levels of the proper weight and grade would see little benefit in a aftermarket cover. Specifically just with the intent of dropping the operating temps a few degrees.
Over it's lifetime, you might see a difference in the most extreme use. Other than that, it is only worth it if you think you need it for one of the above other, rather limited (imho) purposes.
And thus, this is only an answer or purchase decision that you, as an individual can make.
