My experience with tumble dryers is that the non-heat-pump types have a very high temperature at the end of the cycle. If you wash at 40 degrees Celsius, the drying probably reaches temperatures of 70-80 degrees Celsius if your dryer doesn't have a heat pump. Shortening the tumble dry time to leave the clothes slightly moist could reduce the temperature at the end of tumble drying cycle.
The real fix, however, is a drying method that never reaches high temperatures:
- Either a drying rack.
- Or a tumble dryer that has heat pump. Heat pump tumble dryers can make your clothes dry without reaching temperatures of over 50 degrees Celsius.
Heat pump tumble dryers are more expensive, though, and less durable (since they have a heat pump, which is a complex piece of technology as opposed to a simple resistor).
If neither of these two is not a possibility for you, you could of course ask why drying racks are not permitted. If it's due to moisture concerns, perhaps you could use the tumble dryer in a shorter cycle to make your clothes only very slightly moist as opposed to completely dry (thus reducing the temperature at the end of the drying cycle), and then use drying rack with very slightly moist clothes. That probably causes less issues due to moisture than drying fully wet clothes.