Abstract The equation for the temperature distribution in a uranium rod under transient conditions is subjected to the finite Hankel transform, to produce a formal relationship between the physical parameters of rate of heat production, rate of heat removal and the temperature at any point in the rod. The form of solution is then applied to find the changes in uranium surface and centre temperatures following arbitrary changes in the rates of heat production and heat removal. The method is an inverse one in that arbitrary forms are assumed for a function φ(t) which is introduced into the equations, and the resulting variations of uranium temperature and rates of heat production and removal are examined. Within this limitation, however, the temperature and reactivity changes within the reactor can be determined for a short period of time following a disturbance, during which the relatively small thermal capacity of the uranium makes it the dominating variable.