The traveling fire methodology provides more realistic fire scenarios for structural fire design by considering fire dynamics in large compartments which are beyond the validity or scope of conventional structural fire design codes. This novel methodology developed recently elsewhere has been implemented in the OpenSees software framework. In this work, effects of traveling fires on the thermal responses of a large composite structure are studied using OpenSees. Finite element analyses are performed to model the detailed heat transfer in the composite structure subjected to traveling fires. It is found that the traditional "equal area" concept is not applicable to evaluate the fire resistance of structures in traveling fires. Results show that traveling fires with larger sizes seem to be more detrimental to steel beams in terms of quicker failure time, while smaller traveling fires produce higher peak temperatures in the concrete slab. Large through-depth thermal gradients are created in the beam sections due to the heat sink effect of the concrete slab, with higher gradients produced by larger fires. The maximum thermal gradients in the concrete sections seem to be insensitive to the sizes of travelling fires.