At most SxS shoots, unless there's a provision for guns other than sxs, you wouldn't be able to use a SBT, even a vintage one.

For the most part, I use trap only to warm up for the Great Northern (mid-June), which has a simulated pigeon ring. Something close to a trap gun, or choked like one, works best.

Re barrels heating up--I always wear a thin leather glove on my left (leading) hand anyhow. And the barrels will warm up enough, especially on a hot summer day, that you may want something that gives your hand more protection--especially if you have a gun with a splinter FE. Like my trap/pigeon ring gun. But I've found they don't get all that hot unless maybe you're shooting a short squad, like 3 guys. Then they will. A full squad, moving after every 5 targets . . . they'll get warm, but I don't need anything more than my thin leather glove.

Back when we used to shoot a flurry event as part of the UP/Great Northern--70-some targets in 2 1/2 minutes, and you could use someone to load for you--then you definitely needed a padded glove if you were using just one gun.