I personally think that it is fine to go to for a Sauna or to the Steam room after anti-wrinkle injections. I have not seen any concrete evidence that it should be avoided and I think that it is purely speculation that you can’t exercise, drink alcohol, lie down or go for a sauna after anti-wrinkle treatments.
I wouldn’t recommend going to the Sauna within 2 weeks of having dermal filler treatment however because of the unknown effects of heat on dermal fillers.