“Electrify everything then decarbonize electricity”. This mantra is popular, but dangerously incorrect for industrial heating. It raises output costs by 10-110% without any material CO2 savings. This 19-page note presents five separate case studies in the steel, cement, glass, petrochemical and paper industries, which exceed 15% of global CO2. Only a CO2 price is likely to maximize efficiency gains across multiple disparate industries.