Sorry, missed on heat pump.
Our croft is kept warm by a ground heat pump. It has two counter pulsation exchange tubes going 260 m down into solid rock. When it was installed, it was calculated for a 160 sqm house, but despite the croft only being 56 sqm there are days when the temperature falls to 19.5 °C; consequence to that it’s a draughty log house, which is not protected from winds coming in from SSW. The outdoor sensor and those on the radiators all agree on that the temperature is the stipulated 21 °C, as they don’t react to draught.
Air-air heat pumps have exactly the same problem: they require good insulation, or heating can become costly. Assuming that your floor area is 170 sqm (ceiling height of around 3 m) and an effect need of 70W/m (older Finnish/Norwegian/Swedish house), there would be a need for a 12 – 12.5 KW heat pump. If your barn is not insulated a 20 KW pump might perhaps be required.
London, UK; Boston, MA