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.

Being that the recommended max temperature for hot tubs is 104F that could be an issue. Hot tubs are definitely more pleasurable than saunas, and if it comes "close enough" I'd be fine with that.