An apparatus for forming, by a chemical vapor deposition process, a thin film of crystals such as diamond on a surface of a heated substrate placed in a reaction vessel. The apparatus has a substrate supporting structure, a heater for heating the substrate by heat conduction or by electric current supplied directly to the substrate, and a cooling device for cooling the substrate. The heater is controlled in accordance with the measured temperature of the substrate so as to accurately maintain the substrate temperature at a constant level.