I can't picture how a locked or welded axle can make more heat than an open one.

One could guess maybe the lack of differenal ability would cause a constant, but subtle, amount of l/r torque bias. It would depend on how much cornering you were doing, or even the minor differences in tire height. Figure eights in a asphault parking lot would cause more heat from a welded rear than an open one. And minor tire differences would be corrected with normal driving (left and right turns) and by normal tire scrub, but there is still a minor amount of force exerted on the diff that would not be there if it was open.

While neither of the above possibilites are major problems, they may be enough to cause a bit more pressure between the ring and pinion gears.

My guess is that the temp described is normal and may even be related to the gears going through a small break in peroid to account for the welding and any warpage or reassembly difference from stock. I would also guess it will go away (or become a huge problem) in 500 miles or so. I would suggest maybe changing the oil now and then at that 500-1000 mile mark. Just use the cheapest stuff you can find (Wally World) for this change and then go back to whatever flavor you like. This will also allow for a clean out of any residual crud from the welding process.

Michael