As a long-time cyclist in Mississippi who rides year-round, I end up acclimating to the heat every year, and I ponder these very things.
I think it's an additional stress, and something that has to be factored in. Your body can only handle so much stress productively. Beyond that, you spend more time recovering than the adaptations you get in return. So, it depends on how much of a priority the training adaptations is, i.e. that you're trying to get faster, stronger, greater work capacity, etc. For example, if I was on a barbell strength-building program, I wouldn't put any value in doing my barbell lifting in hot conditions; I would put ALL my effort and recovery resources towards the actual strength work. But if I was on a program to prepare myself for a summer of outdoor labor, I would certainly do some kettlebell carry, conditioning, etc. outdoors in the heat or as much as possible in the conditions I had to perform in. In that case, the heat is part of the productive stress towards the end objective.
All that said, as long as I get outside and keep riding with the seasons, I don't notice very much difference in my cycling in cool weather vs. hot. If my average speed is 18 mph avg on a 2 hour ride, on a perfect cool-weather day I might have a 19 mph avg and feel more fresh, and on a really hot brutal day I'll still be 18 mph but it'll be a harder effort and I'll be a bit more wiped out afterwards. So the only time the heat is REALLY a factor is if I haven't had a chance to acclimate to it, it's a REALLY hot day, and I try to ride my same average speed or higher. Then I might red-line and the day gets very miserable very fast. Have only experienced that a handful of times and would not recommend.
So, to your question "if a person becomes well conditioned working out indoors, will that conditioning carry over to outdoor activities In the heat just as much as if the person had worked outside all along?"... mostly I think it will, but the heat can be a factor if they push themselves too hard, it's very hot, and they're not at all used to it.