Using the width of concentric grabens formed during the relaxation of the Asgard basin on Callisto, in combination with rheological flow laws of ice and laws concerning the variations in strain rate around a relaxing crater, the surface thermal gradient of Callisto at -4 b.y. is estimated to be near 0.5¿K km-1. It is assumed that the graben width depends on the depth of the brittle/ductile transition zone. Around the Asgard basin, the depth of this brittle/ductile transition zone varies from 23 km (at 200 km from the crater rim) to 4 km (at 800 km from the crater rim). It is assumed that the thermal characteristics were constant over the extended zone and that the difference in the depth of the brittle/ductile transition zone is only due to differences in the strain rate around the basin during the relaxation of the initial cavity. Calculations show that Newtonian flow law for ice gives a strain rate of external relaxation at the crater rim of about 10-14 s-1, while a power law gives a strain rate of about 10-6 s-1, assuming a surface temperature between 100 and 150¿K. The order of magnitude of the calculated thermal gradient is independent of the chosen flow law. This calculated gradient is, however, one order of magnitude lower than those calculated theoretically with a chondritic abundance of radioactive elements in the silicate part of Callisto. ¿ American Geophysical Union 1991