But really, did the earth stay hot enough for "a few million years" - hot enough to affect the locked side of the moon more than the other?
The moon has no atmosphere, thus radiation from the earth cannot affect the far side of the moon at all. So obviously, even to this day, the earth still affects "the locked side of the moon more than the other". The question is simply how much. The moon and earth were both molten after the collision, so it was not a matter of the earth being hot enough to melt the moon, but merely the earth imparting energy to prolong the cooling of the near side. No matter what, the near side must have cooled slower than the far side - it's a straightforward matter of thermodynamics. One side of the moon was receiving energy from the earth while the other side was not. The near side didn't need to stay so hot it was incandescent, but merely "softer" so that small impacts would heal more on the near side than the far side, and the duration only needed to be long enough to result in some degree of visible difference, which is what we still see today.
The whole thing sounds plausible to me.