Relevant quantities in transient heat conduction within solids include the temperature distribution and the total energy released up to a given time. Expressions for these quantities are well known in the case of large plates, long cylinders, and spheres initially at a uniform temperature and subject to convective boundary conditions. Because the heat transfer coefficient usually is not known accurately, it is of interest to assess how the uncertainty associated with its estimated value propagates into the uncertainties of the local temperatures inside these three bodies and of the total energy released from them. In this paper a calculation procedure in agreement with current international recommendations is developed for this purpose.