Inside the house 10° warmer than outside - how does that happen?

Hello!
We are beginners in "living in a new building" and the first spring is raising questions.
Our heating (Tecalor THZ 504) has long since decided, based on the outside temperature - currently about 20°C - that it is summer operation. In other words, the heating is not running.
The system information still shows the flow temperature at just under 30°C, but the volume flow has dropped to 0.

What is still running is the ventilation, and I suspect our heat recovery is the problem – because what use is the air exchange with outside if it pushes the air back inside at almost the same temperature as it lets it out?
We only have one outdoor temperature sensor. The device is somehow dumb when it comes to the indoor temperature. It claims that the actual temperature is 20°C. However, it apparently also notices (through measurement) that the exhaust air temperature is just under 28°C. This is also confirmed by our various thermometers in the house.

The question remains: Why do we even have 28°C in the house? Where does it come from?
Can this be caused purely by solar radiation through the windows?

We have an air conditioner, but I don't particularly want to run it yet when it's only about 20°C outside and raining.
How do you other "new building owners" solve this problem? Shading? Something else? Or do you not have this problem and something is wrong with our house technology?
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The heating system still produces hot water, so it won’t be inactive for half a year now. This is the sun. How is the shading situation with you?

Is there (no) summer bypass for your ventilation system?

Is there (not) a summer bypass for your ventilation system?

There is a "Bypass" setting on the ventilation system, yes. But I can't find anywhere in the user manual what that means. So in the ventilation settings there is a value called "Passive cooling," and you can set it to: "Off, Exhaust air, Supply air, Bypass, and Summer cassette." I have already googled "Summer cassette," and we would have to replace a part for that, which is too tricky for us (not really allowed for amateurs), as you risk damaging the heat exchanger if you remove/store it. I don't know how our warranty stands if we tamper with it ourselves. Unfortunately, the user manual says absolutely nothing about all of this.

The heating still produces hot water, so it won’t be inactive for half a year now.

That’s the sun. How are things going with the shading on your side?

Wow, we barely dealt with shading – but we do have roller shutters that we could close if needed. But would that help?
I’m just amazed that it’s significantly warmer inside the house than outside. We never had this problem (of course) in the 1992 house.

That brings massive benefits and without it you will be cooked or have to cool against it