A hand calculational procedure used to estimate the gamma and neutron heating in and about a homogeneous reactor core is described. It affords a good insight into the physical processes involved, can handle complex geometries, and is relatively simple to do. One of the interesting results of the gamma heating part of this calculation is the heating of high-Z materials. In an example which is used for a medium-Z element, such as molybdenum, the gamma heating is four times more per unit mass than it is for a substance such as graphite. For higher-Z materials the heating is proportionately greater. One of the interesting results of the neutron heating part of the calculation is the heating of low atomic weight materials. The heating in water from the moderation of fast neutrons, for example, is found to be three times greater than that of the gamma heating.