https://www.nytimes.com/2009/02/03/health/03real.html : "In one study by Austrian researchers, for example, a group of 50 adults were split into two groups and tracked for six months. One group was instructed to use saunas regularly; the other group abstained. At the end of the study the sauna group had contracted fewer colds. “This was found particularly during the last three months of the study period, when the incidence was roughly halved compared to controls,” the scientists wrote. Other studies have found similar results. But doctors caution that saunas can be hazardous to those with heart or circulatory problems."
https://www.healthline.com/health/can-you-sweat-out-a-cold#s... : cites the same study and says it may prevent colds, but cites one study saying that hot dry air specifically (3-minute exposures thereto) doesn't help... seems not the regular kind of sauna: "Use of this type of sauna has little in common with that of a regular sauna, where one usually stays longer than 10 minutes and sweating is desired." Hmmph. I'll say that one is only partly relevant.
And the "Other studies have found similar results" link's abstract says this: "The common cold has great socio-economic impact. To date, no prophylaxis has been scientifically shown to be effective. A number of older reports implied that visits to the sauna and other thermotherapeutic measures might provide a certain degree of protection. More recent data suggest that this supposition is probably true. Nevertheless, there are a number of important questions still to be answered in this area."
The cited study 1990 https://doi.org/10.3109/07853899009148930 is evaluating "consistent sauna use preventing colds" rather than "get in the sauna to sweat out a cold", and in fact stated that
"The average severity of the common colds per cent
was 1.8f0.8 in group 1 and 2.0k0.7 in group 2. The
mean duration of common colds per event was 6.7 k3.9
days in group 1 and 7.5k5.6 days in group 2. Neither
yields a significant difference between the two groups."
So, that one study found a minor preventative effect, but no curative effect.
Interesting that they also state
"The average frequency of sauna bathing was 26.8 55.5
(mean k SO) per six months. The frequency of common
colds during this time was 33 in group 1 and 46 in group
2. This difference between the two groups is statisti-
cally significant (P <0.05). The expected frequency ac-
cording to previous reports (1-9) and based on the six
months preceding (Table 1) the study would be 50 per
six months in each group."
They expect 50 colds per group of 25 people in six months? On average each person getting a cold for a week every three months?
Looks like that's not far off, depending on the age distribution. Kids 4-8 per year, over 60 maybe 1/year. Wow.
https://www.nytimes.com/2009/02/03/health/03real.html : "In one study by Austrian researchers, for example, a group of 50 adults were split into two groups and tracked for six months. One group was instructed to use saunas regularly; the other group abstained. At the end of the study the sauna group had contracted fewer colds. “This was found particularly during the last three months of the study period, when the incidence was roughly halved compared to controls,” the scientists wrote. Other studies have found similar results. But doctors caution that saunas can be hazardous to those with heart or circulatory problems."
https://www.healthline.com/health/can-you-sweat-out-a-cold#s... : cites the same study and says it may prevent colds, but cites one study saying that hot dry air specifically (3-minute exposures thereto) doesn't help... seems not the regular kind of sauna: "Use of this type of sauna has little in common with that of a regular sauna, where one usually stays longer than 10 minutes and sweating is desired." Hmmph. I'll say that one is only partly relevant.
And the "Other studies have found similar results" link's abstract says this: "The common cold has great socio-economic impact. To date, no prophylaxis has been scientifically shown to be effective. A number of older reports implied that visits to the sauna and other thermotherapeutic measures might provide a certain degree of protection. More recent data suggest that this supposition is probably true. Nevertheless, there are a number of important questions still to be answered in this area."
Sounds like there is mild evidence in favor.