The unsteady heat-transferprocesses from oblate or prolate spheroids, at the limit of very small Peclet numbers is examined. A perturbation technique for the temperature and the geometry of the particle is used to obtain the rates of heat and mass transfer, first in the Laplace and then in the time domain. A solution to the problem is obtained, including the epsilon(2) contribution (epsilon is the eccentricity). The solution reveals the existence of several history terms, which are analogous to the history terms of the creeping flow equation of motion. One of these terms is solely due to the eccentricity of the spheroid. This is an indication that the shape of the particle is a factor of the existence and form of history terms. In addition, an exact expression for the steady-state heat transfer from a spheroid is obtained using a convenient transformation of the heat-transfer integral.