Although a variety of methods to predict the effective thermal conductivity of porous foams have been proposed, the response of such materials under dynamic compressive loading has generally not been considered. Understanding the dynamic thermal behavior will widen the potential applications of porous foams and provide insights on methods of modifying material properties to achieve desired performance. Previous experimental work on the thermal conductivity of a flexible graphene composite under compression showed intriguing behavior: the cross-plane thermal conductivity remained approximately constant with increasing compression, despite the increasing mass density. In this work, we use molecular dynamics (MD) simulations and finite element analysis to study the variation in both the cross-plane and in-plane thermal conductivity by compressing isotropic graphene foams. We have found that, interestingly, the cross-plane thermal conductivity decreases with compression while the in-plane thermal conductivity increases, hence the dynamic thermal transport of the graphene foam becomes anisotropic with significant anisotropy ratio. Such observations cannot be explained by the conventional effective medium theory, which describes the increase of thermal conductivity to be proportional to mass density. Thus, we propose a model that can describe such anisotropic effective thermal conductivity of highly porous open-cell media during compression. The model is validated against the MD simulations as well as a larger-scale finite element simulation of an open cell foam geometry.