For perspective, a commonly found alternative system is that the heating gets turned on at a particular date (say October 1) every year, regardless of weather, and off again at a particular date in the spring - and if you are cold before or after that, put on a sweater! Not that this is necessarily legally supportable either - doropfiz is right, the Mieterverband/Asloca is the appropriate place to go for more information - but just to give you an idea what other approaches you are likely to encounter in your housing search.
I really suspect there is a misunderstanding here, and that the heating is turned on when the external temperature falls below a certain threshold for a certain number of days - not the temperature in your living room.
Yes, as MathNut says, the systems can vary. Either by date, or by some variation of "the heating is turned on when the external temperature falls below a certain threshold for a certain number of days".
Within that latter,
the "external temperature" may be 10 or 13 or 15, for example.
the "number of days" may be 2 or 4 or 6, for example.
Some heating systems do this switching automatically. Even so, the variables are set by the caretaker based on experience with the specific building, or with a cluster of buildings in a complex.
Once Autumn starts its decent into the cold, there are a few weeks of temperature confusion, when the heating system may come on, and then switch off again, before it comes on again, according to fluctuations in the weather. That's the time to make sure you have your warm clothes ready for Winter.
When Spring bursts free, there are some similar weeks, when one is caught between "what? they've switched off the heating?!" and "oh, good, it's on again" through to "enough already, Summer's arriving!"
During those transition weeks, the hot water supply may be a bit odd, too, either because it may be technically related to the heating system, or because the change in weather influences people's use of hot water.
All in all, though, most Swiss buildings are heated comfortably enough, and it is perfectly reasonable to expect to to add a pullover and longs and socks in Winter. A home need not be so over-heated that one can get by, even in Winter, wearing only shorts and a T-shirt when at home. Of course, if the weather itself permits that, wonderful, but it needn't be expected of the building's heating system.
As a guide, our (heat pump under-floor) heating is on all year, but switches itself on and off as necessary - and that necessary is if it is 16° or less for more than 12 hours.
Inside it‘s usually around 23°...
Same with us, doors still open.
Last week I was in the following places, Geneva, Gstaad (took the long way to Bern on the MoB - amazing) Bern, Zurich. Arth-Goldau. Everywhere the temperature was 20c +. So good advice to open the windows.
Of course if you're living on the Jungfraujoch I can understand you're feeling cold!!!
Instead of relying on the EF panel of armchair experts, suggest you read this article which explains all. If you don’t know German then Google Translate is your friend:
Still, OP isn't even sure whether those 13°C are indoors (highly unlikely) or outdoors.