David Roche, a notable running coach (and runner), and his co-coaching wife (and runner) Dr. Megan Roche (MD/PhD) seem to think that hot tubs need to be at least 106F to generate much of a heat shock response, which is normally what one is looking for in the context of post-exercise heat exposure. I should note, however, that they are mostly reading the same research papers as everybody else, not doing primary studies themselves.