Heating demand is broadly divided into low-temperature demand for space and water heating, and high-temperature demand for process heat in industry.
Time series of low-temperature heating demand can be approximated by the degree-day assumption, which assumes that heating demand increases linearly with temperature below some threshold (e.g. 15 degrees Celsius). Temperature is averaged over a day, then multiplied with an intraday profile that reflects consumer behaviour (e.g. consumers may turn down their heating at night).
Eurostat yearly energy consumption
For years 1990, 1995, 2000, 2005, 2008-2014
Covers energy usage in EU, Balkans, Norway, Ukraine, Turkey, but NOT Switzerland.
Distributed by sector (Industry, Transport, Residential, Services).
Q: Is there any non-electric residential and service energy consumption other than low-T heating and cooking with natural gas?
Odyssee-Mure database yearly energy data for Europe
This distinguishes between water and space heating by sector (Residential/Tertiary/Industry), but is incomplete (missing countries and years).
BMWi yearly energy statistics for Germany
BMWi energy statistics
This distinguishes between water and space heating.
Heat demand in Aarhus, Denmark
Apparently available here: