Should the inverter be placed outside?

At some schools around here, the inverters are mounted outside, not always fully weather-protected either. Seems not to be a problem.

But: my inverter is very loud. No problem in the technical room in the basement, but hanging it outside would be more of a nuisance than the heat pump.

It also makes noise complementarily (when it is bright and warm) to the heat pumps (when it is cold and dark outside)...

I would pay close attention to that, especially if it is a larger one.

At first, I thought of the battery as maybe just 5-7kWh.

Why? Why not directly 25kWh. It's not much more expensive either. If you’re doing everything yourself anyway.

Has anyone here already had experience with the heat of the inverter? How would you approach the matter? The battery storage must of course be in the technical room, it cannot be moved out.

At full power, there is always heat generation in the inverter, which can vary significantly depending on the device type and dimensioning. With 2 inverters and a total of 38kWP, you can already expect a certain heating capacity that will warm the technical room well. A plausible approach with a little over 2% electrical efficiency loss at full load would suggest a heating capacity of about 1kW. For context: This can keep a 40 sqm room in a KfW40 house at 20°C when the outside temperature is 0°C.
Many inverters are designed to IP67 and can easily be mounted outside. I would still give them a small roof to avoid direct sunlight and direct rain. Whether you screw them to the house wall or to a separate frame so as not to alter the house build does not matter.
In combination with an AC storage, I would prefer outdoor installation.

No, nothing fluctuates significantly. Modern inverters have efficiencies between 96 and 98%. Period.

That means with 38kWp and a deliberately high-quality selected inverter, you are at 0.7-1.1 kW. And it does produce this heat because it can’t be avoided. By the way, the losses in an inverter do not scale so much with power, because switching losses mainly play a role.

So it’s best not to think about it too much but mount it outside. Where should the problem be? Wallboxes, outdoor sockets, submersible pumps... you can make electrical devices waterproof. IP67 or if necessary even IP69.

No, nothing fluctuates significantly. Modern inverters have efficiencies between 96 and 98%. Period.

The inverter with 96% efficiency has 100% more heating power than the inverter with 98% efficiency. And you talk about no fluctuation?

Can you maybe reveal a bit more about that? Room size? Ventilation system? KfW40? Domestic hot water heat pump installed? They extract heat from the room.

Gladly: 13 square meters in the basement Insulation meets KFW40 standard Controlled residential ventilation present No domestic hot water heat pump I touched it today when about 20kW were running. Slightly more than hand warm. The inverter is a SolarEdge SE25K-RW00IBNM4, operated with SolarEdge power optimizers (in case that should be somehow important...). The efficiency according to the manufacturer is a "unique" 98.3%