OK, I built a hot wire foam cutter.
Plastic box found. Power connector from busted PC power supply, bought light dimmer for 9 euro. Connector is standard audio connector which is widely available, but good enough to transfer power and current required for the job. Transformer is taken from my DIY soldering iron (200V to 24V). I wired it in following order: power socket -> dimmer -> transformer -> connector. This power supply is powering my soldering iron too. Turn dimmer to max power for soldering, turn down for foam cutting.
The cutter itself later on.