A method of filling a tank container of a vehicle with gaseous hydrogen from a storage container of a supply station, wherein the method comprises the steps of: - connecting the storage container to the vehicle container by means of a filling device, of which the hydrogen flow is regulated by means of a valve controlled by a control device, - determining a parameter value for the heat dissipation characteristic of the vehicle container, - recurring sensor-based detecting of actual values of the temperature and pressure of the hydrogen in the vehicle container at discrete times t i, - recurring determining of a forecast value of the temperature and pressure of the hydrogen introduced into the tank at discrete future times t i+1, - periodic determination of the filling state of the vehicle container during the filling of the vehicle container, wherein an activation signal is output to a cooling device set up for cooling the hydrogen present in the supply station at a time t i as soon as at least one actual temperature value of the hydrogen in the vehicle container detected for a time t i exceeds the forecast value of the temperature of the hydrogen in the vehicle container determined for the same time t i by a differential limit value determined based on the parameter value, or as soon as at least one actual temperature value detected for a time ti exceeds a first absolute limit value determined based on the parameter value, and the refrigeration capacity of the cooling device for subsequent times t i+k, (k≠0) is readjusted in such a way that the forecast values of the temperature of the hydrogen in the vehicle container determined for the times t i+k do not exceed a second absolute limit value. - connecting the storage container to the vehicle container by means of a filling device, of which the hydrogen flow is regulated by means of a valve controlled by a control device, - determining a parameter value for the heat dissipation characteristic of the vehicle container, - recurring sensor-based detecting of actual values of the temperature and pressure of the hydrogen in the vehicle container at discrete times t i, - recurring determining of a forecast value of the temperature and pressure of the hydrogen introduced into the tank at discrete future times t i+1, - periodic determination of the filling state of the vehicle container during the filling of the vehicle container, wherein an activation signal is output to a cooling device set up for cooling the hydrogen present in the supply station at a time t i as soon as at least one actual temperature value of the hydrogen in the vehicle container detected for a time t i exceeds the forecast value of the temperature of the hydrogen in the vehicle container determined for the same time t i by a differential limit value determined based on the parameter value, or as soon as at least one actual temperature value detected for a time ti exceeds a first absolute limit value determined based on the parameter value, and the refrigeration capacity of the cooling device for subsequent times t i+k, (k≠0) is readjusted in such a way that the forecast values of the temperature of the hydrogen in the vehicle container determined for the times t i+k do not exceed a second absolute limit value.