Industrial greenhouse gas emissions, primarily carbon dioxide, constitute about one-third of global emissions, and 75% are caused by the generation of heat from fossil fuels. Therefore, a key decarbonisation strategy is electrifying heat generation using renewable sources and power-to-heat technologies. This study explores the impact of the energy price on the optimal choice and sizing of power-to-heat and storage technologies in existing energy-intensive industries with a variable heat demand. A mixed integer linear program is used to determine the technology portfolio and size of the equipment that leads to the lowest total annual cost of the utility system while ensuring that heat demand is always fulfilled. The results of a case study in the Netherlands show that adding power-to-heat and storage technologies to a fossil fuel-based combined heat and power plant is economically viable under all explored scenarios. The mean and the variance of electricity prices significantly influence the sizing of heat pumps, electric boilers, and thermal energy storage. High and stable electricity prices lead to larger heat pump capacities compared to scenarios with low and more variable electricity prices. Electric boilers are primarily sized based on the variance of electricity prices and the capacity of thermal energy storage, which plays a crucial role in managing electricity price fluctuations. The study emphasises the potential for cost-effective electrification and provides valuable insights for reducing industrial CO₂ emissions.