Heat conduction between fractal soot aggregates and the surrounding gas is one of the fundamental problems encountered in the theoretical analysis of soot particle size measurement using the laser-induced incandescence (LII) techniques. Improved the modelling capability of this fundamental phenomenon helps improve the accuracy of LII based techniques for soot particle sizing. Heat conduction rate between fractal aggregates and the surrounding monatomic gas in the transition regime was calculated using the direct simulation Monte Carlo (DSMC) method. The fractal aggregates were numerically generated using a combination of particle-cluster and cluster-cluster aggregation algorithms. The DSMC results were analyzed using the Fuchs approach for heat conduction between a spherical particle and the surrounding gas in the transition regime to arrive at the size of the heat transfer equivalent sphere for fractal aggregates. The heat transfer equivalent sphere radius for fractal aggregate is required in the formulation of aggregate based LII models. Such heat transfer equivalent sphere radius is recommended as the characteristic length scale of fractal aggregate heat conduction and is compared with the radius of gyration and the projected area based sphere radius.