As part of the decarbonization of its existing building stock the UK needs to replace gas boilers with heat pumps and low-temperature heat networks. Both technologies are efficient at supply temperatures of 55 °C, with a maximum of 70 °C for heat networks, when existing systems have been designed to operate at 82 °C. Most space heating systems are expected oversized and operate most of the year in part-load, which facilitate the temperature reduction, but little is known about the degree of oversizing. This paper uses the case study of a pre-1919 school in Edinburgh to evaluate the true oversizing of its heating system and its consequences on minimum supply temperatures. This building is still equipped with single glazing and is therefore a worst-case scenario. An oversizing of 32 % was estimated which enables the use of a supply temperature below 70 °C all year round. Moreover, the supply temperature can be kept below 55 °C all year round during daytime due to internal heat gains. In conclusion, this building shows a nascent readiness for low-temperature heat. It would benefit from energy efficiency measures such as double-glazed windows, but this is not pre-requisite. Those results are important for the heat network industry when sizing their systems, but also energy and asset managers when they schedule renovation programmes to have their buildings low-temperature-ready.