Another (minor) data point. I live in South Florida so almost my training is in hot weather. Today it will be around 90 when I start my afternoon run. From skiing in the Rockies to skiing and hiking in the Alps, I’ve never had the slightest problem with altitude. I haven’t been as high up as Roxanne, but I have done a couple 4,000 meter climbs and have spent a fair amount of time above 3,000 meters. It would be great if this heat cross training is valid.
Living in South Carolina, I have some anecdotal experience with this “method” and doing high altitude mountain running races. I think there is is some benefit, but it’s really hard to measure because:
A) some of what you’re getting is just general “heat acclimation” advantage because high-altitude races are often in low-humidity climates, making the race environment much more conducive to hard work than the training environment.
B) everyone’s response to both the heat acclimation and race-altitude can be so different.