Can the apartment ventilation system of controlled residential ventilation enter the sheds?

Enclosing and insulating would not be a problem. : do you mean by "entire technology" only the technology of the controlled residential ventilation, or further (heat-generating) technology? I have now checked the first Google hit device, it says "Operating temperature: +5 °C to +40 °C". So frost-free. That should be doable, if necessary with a frost guard for three really cold nights a year (Rhineland).

Hi. Heat pump, controlled residential ventilation, router, switch, electrical distribution. Inverter plus battery. So enough waste heat is generated...

Hi. Heat pump, controlled residential ventilation, router, switch, electrical distribution. Inverter plus battery. So enough waste heat is generated...

The question would rather be whether it doesn't get slightly >40°C in summer...

I can't (may not) say it with just one word, but: Nope

Weren't there threads in this forum about controlled residential ventilation in the attic? It should be similarly designed. I seem to remember that there were some moisture problems and also forum members who built a separate enclosure for the device in the attic. We also wanted to put the device in the attic at first, but decided against it because of the cold floor (frost/moisture).

My controlled residential ventilation system is located in the attic in the warm roof. The ventilation ducts run from the insulated area into the cold area. There, all supply and exhaust air ducts are insulated with aluminum-coated mineral wool. The outdoor air and exhaust air ducts are insulated with Armaflex. I have no problems with moisture in the ducts.