Heat gain in hyperbaric chambers may lead to hyperthermic fatalities. Several case reports were published, where chamber occupants died from heat stroke. In six out of eight cases, the victims were recompressed on return from their dives in poorly cooled deck chambers in tropical climate latitudes. Recompression started at ambient temperature. As pressure affects the heat conductivity of the breathing gas and grossly influences the effectiveness of the physiological modes of heat dissipation, chamber temperature as a function of pressure and pressure time course is crucial. The above mentioned fatalities prompted the analysis of the thermodynamics of the chamber compression process. An analytical expression results, that describes how temperature changes as a function of compression rate and final chamber pressure. The present law was tested in a hyperbaric chamber at various pressurisation rates and pressures. Conformity of the predicted temperatures and measured values was exceptionally good, with maximum deviations of less than 0.8°C. Chamber temperature can now be predicted from final pressure and compression speed, and thus may help to avoid the occurrence of heat stroke.