Heating device in particular for gaseous fuels

The heater (10) has fuel intake (42) and outlet, and coolant intake and outlet (56,60). It has an internal section (68) with cylindrical wall, which defines a fuel passage between intake and outlet and separates it from a coolant passage. A control device generates or prevents a coolant flow through the passage, dependent upon fuel temperature. The internal section has radially projecting fins defining the fuel passage. The heater can be connected to the housing (36) of a pressure regulator (18).