A measuring device for determining the temperature of a medium in a container or a pipe has at least one temperature sensor, arranged on the outside of a container or pipe wall; an output for the temperature registered thereby; and an output for the measurement result obtained thereby. The device connects at least one first differentiator, capable of determining at least one first derivative of the progression over time of the temperature registered by the temperature sensor; at least one first multiplier for multiplying the derivative by a first factor which is a value for the time constant of the heat transfer through the wall; and at least one adder, between the output of the temperature sensor and the output of the measuring device.