We solve the two-dimensional time-dependent heat flow equation across an idealized fracture zone boundary, which includes the process of lateral heat conduction across an initially abrupt temperature contrast. From this solution we can calculate the temperature field for any initial offset and at any sequential time. We can use this to calculate a theoretical free air gravity anomaly across the fracture zone given an assumed density variation with temperature. Results for a 30 m.y. initial offset show that both the ampltitude and the shape of the anomaly are significantly altered by lateral heat conduction across the fracture zone even during the first few million years. Assumptions of a sharp density contrast across fracture zones are therefore only valid in very restricted regions close to the ridges. We also find that the theoretical anomaly is small in comparison to observations of free air gravity anomalies. These results add significant complications to attempts at finding unique models for the structure of the lithosphere from gravity anomalies across fracture zones.