There is a cast bullets forum on yahoo somewhere. Heat treating cast bullets is fairly common among those who use cast bullets for precision shooting in Cast Bullet Assoc competition in the plain-base matches, BPCR, and modern Schuetzen (ASSRA/ISSA etc.)
In Schuetzen we tend to use very low percentage tin/pure lead alloys. 25 or 30 to one. Just enough tin to give complete filling in some of the old turn of the century multi-diameter bullet moulds. We also use dead soft alloys since we mechanically pre seat the bullet into the throat of the chamber before inserting a primed and charged cartridge case. Old time muzzle/breech loading schuetzen experts also used dead soft alloys since they were in essence muzzle loading a lubricated, very tightly fitted, bullet, sans patch of course, (using a carefully fitted false muzzle and a mechanical starter for ultra-precise alignment) down to the mouth of a plugged case, which was then removed, and a primed charged case inserted.
There is some evidence that lead, unless it is laboratory-pure quality, almost always has some other elements in the mix. Any impurities can contribute to varying degrees of hardness. Certainly most scrap lead has been melted and remelted who knows how many times. Whether it is enough to influence ballistics, by changing the the weight or penetration because of hardness in all truth is probably pretty moot. Since in most cases the ball is bore diameter or less and it is the patch that engages the rifling, the harness of the lead in that regard is immaterial--it seem to me.
Lead bullets and balls can be dropped into a bucket of cold water (making @!*% sure it won't splash into your melting pot) and you will get a (modestly) harder ball or bullet ---"chilled shot". Some schuetzen and BCPR guys chill their bullets if they are pushing velocities a bit and want to avoid overdriving the rifling and getting leading as a result
By the same token you can reheat a bullet and let it air cool and it will anneal/soften it somewhat. I make up batches of my schuetzen bullets during the winter. I sort them by weight and store them in a freezer, which is supposed to stabilize or at least slow any alloy drift. then a week or so before a match I'll take a couple hundred out and put them on cookie trays and heat them to about 350 for half an hour or so and then let them air cool then pan lube them. In theory that should give me a reasonably uniform alloy temper bullet to bullet. I'm not sure it affects my scores, but there are a LOT more issues involved than my bullet alloy and temper