Solutions are given for a number of one‐dimensional problems in heat conduction arising in connection with extensions of the flash method of measuring thermal diffusivity: conduction through slabs of one or two materials, with flash or step irradiation of the front surface, with and without thermal losses from the surfaces, with and without interior contact thermal resistances. The treatment involves application of Laplace transform methods, but with the usual inversion of the transform by integration in the complex plane replaced by a convenient expansion of the transform that permits term‐by‐term inversion by use of standard tables. This yields the temperature rise on the back face of the slab as a series of terms that converges particularly well at low values of the time, in contrast to the commonly used solutions. In many cases one to three terms suffice to give good results, even for times well in excess of the half‐rise time for the temperature on the back face. The advantage of using step irradiation instead of flash irradiation is indicated briefly.