The question is not where the heat went beforehand, but rather where it first came from. I already told you this before. Once the universe was there, the cooling was automatic (initially due to the transformations between all types of particles). The question is where it all came from to begin with, and that we don't have an explanation for. The only viable scientific hypothesis to explain this, as I noted above, is that of string theory (I ever-so-slightly favor the ekpyrotic scenario myself). But regardless of where one posits that the initial conditions emerged from (God works just fine, so far as we know at this juncture) the rest is self-generated.
Do we have any examples in the lab of matter cooling due to particle transformations rather than through heat transfer?
Me too, mostly for aesthetic reasons. Actually I like the earlier oscillating universe scenario, before branes got dreamed up. But the way things are going, I don't see how to get there from here. (I don't know how we got here from there, for that matter, but I'm content to follow the evidence, even if the universe doesn't bow to my personal preferences.