Industrial process heat dominates manufacturing emissions in the EU. Yet, there are readily available solutions that can continuously generate process heat. Industrial heat pumps and heat batteries paired with on-site solar PV can be a solution to bring power to heat generation quickly and cost competitively with natural gas. Using a dataset of 2,192 facilities of different manufacturing sectors from Climate TRACE, each facility is modelled with co-located, off-grid solar PV with industrial heat pumps and batteries installed in 2030. Under this modelled configuration, 58.8% of fossil-fuelled process heat can be decarbonised using solar PV within a 5 km buffer zone around each facility site at an average levelised cost of heat of €55/MWh. After expanding the buffer zone to 15 km, the share of possible decarbonised heat rises to 84.4% of process heat at €62/MWh against an EU average gas-heat cost of €93/MWh. Each facility is optimised to provide the highest availability and highest savings under its country's gas costs. These results show that Southern Europe can cost-competitively decarbonise over 95% of its heat demand. Central Europe (Rhine-Meuse Region), where most of the large, heat intensive sources are located, can decarbonise over 70% of its heat demand using on-site solar plus storage.