An apparatus for monitoring and controlling the operation of an electrical power transformer includes a processor with input transducers for providing to the processor inputs indicative of electrical current in a winding of the transformer and ambient temperature outside the transformer. The processor is arranged using an algorithm based upon heat transfer to repeatedly calculate a first prediction, based upon the present values of electrical current and ambient temperature, of a time period before the hot spot temperature exceeds a pre-set allowable maximum and a second prediction, based upon the current value of power, of a time period before the accumulated loss of life exceeds a pre-set allowable maximum. If the shorter time period of the two calculations is less than a pre-set value, for example one half hour, the processor generates an alarm signal and a display counting down the time remaining in the period, together with a second alarm signal at a shorter second time of for example one quarter hour.