Don't do this wtihout expert professional advice- so join your local Mietverband, renter's association, who have huge experience with this kind of issue.
Write a diary with the temperature of each room several times a day, with dates.
Old post here with great advice from Dorofiz. Membership is currently free till the end of the year
''The Mieterverband ist not to be confused with the much more recently started competitor (imitation?) organisation, Mieterschutzverband, also sometimes known as Mieterberatung (EDIT: see the warning in Mica's post immediately following this one... in that TV report it says that the Mieterschutz helpline is an expensive minute-cost call, and that anyway in many cases no-one answers, and that the mail responses do not seem professional), of which latter I have never yet heard any good report, although I'm open to hearing otherwise.
To join the Mieterverband:
https://www.mieterverband.ch/mv/mitg...iedschaft.html
With membership, you have free access to legal advice, i.e. you can go to their open legal clinic, wait your turn, have someone look over your papers, and then they tell you how you can go ahead and solve the problem. I think this begins immediately upon joining.
For a small extra fee of about Fr. 15 p.a., you can add on legal insurance that is restricted specifically to issues with regard to rental. With this, a lawyer will act on your behalf, if need be. As far as I can recall, for this there is a 60-day waiting period, and the event must have occurred after that period.
Similarly, some medical insurances offer a top-up module for legal insurance related specifically to issued to do with medical matters, service providers and insurances.
Those are two relatively inexpensive ways to cover the two areas of life in Switzerland which are said to cause the most disputes, for an ordinary individual or family.
Separate from those, personal liability insurance costs more, but is well worth having, for your peace of mind. Some rental agencies even require it of their tenants. And legal insurance for advice and disputes in any area of life, can sometimes be tacked onto the liability insurance. ''