The effect os cooling rate on the intensity of low-field thermoremanent magnetization (TRM) in uniaxial, single-domain magnetite is calculated, using both numerical and analytical techniques. These calculations indicate that when a single-domain assemblage is cooled much more slowly than in a typical laboratory experiment, it can remain magnetically unblocked and in thermal equilibrium with an external field at temperatures significantly lower than the 'laboratory' blocking temperature. Owing to the rapid rise of spontaneous magnetization just below the Curie temperature the TRM can consequently be elevated by several tens of percent over that acquired in the laboratory. The paleointensity obtained from rocks that have cooled in nature over geologic time may therefore be erroneously high, if single-domain particles are the primary carriers of NRM. These calculations indicate that when the ratio of 'natural' to laboratory cooling rates approximately equals 10-11, as in the case of orogenic bodies that have cooled over several million years, the paleointensity obtained by the Thellier method can be more than 50% too igh, unless the role of cooling rate is taken into account.