I'd never suggest it. While I applaud you efforts to share things that help you relax, I would never recommend a hot tub for an infant. If a kid is old enough to converse with you they can tell u they are dizzy or having other early sighs of over heating. Though they might seem to enjoy the activity, they don't understand or appreciate it the way you do but their greater surface area/ body mass makes them more at risk.
Not safe... Eventhough our body tempt is at 98.6, it is internal temperature. The skin tempt is much lower. The 99 deg water is too hot for a nine month old--can cause a rapid rise in internal temperature and thus not recommened... Be safe.... Good luck.