An analytical study of anisothermal phase‐transformation kinetics is described. In particular, the familiar Johnson–Mehl–Avrami equation is generalized to the situation for which temperature increases linearly with time. An exact analysis of the problem is carried out, with the general solution being obtained in terms of one of Horn’s confluent hypergeometric functions. In order to facilitate practical application of the analysis, a number of approximate solutions are also obtained, one which is applicable for small relative changes of temperature and two of which are described in terms of certain asymptotic expansions. Two specific numerical examples are considered which serve to illustrate conditions affecting the relative accuracy of the approximate solutions.