The cooling of igneous intrusions into the lithosphere is treated by a time-dependent analytical model with a varying initial temperature distribution throughout the country rock. One important result is that, for long times after the intrusion, the effect of the intrusion on the surface gradient is approximately the same as for a host rock with a uniform temperature equal to the mean of the initial temperature distribution through that interval. The method is of practical importance because it allows us to study the thermal anomaly produced within the lithosphere by a hot batholith or by an astenolith of long vertical extension just after its emplacement. (C) 2000 CNR.