In this paper we propose a file replication scheme inspired by a thermal diffusion phenomenon for storage load balancing in unstructured peer-to-peer (P2P) file sharing networks. The proposed scheme is designed such that the storage utilization ratios of peers will be uniform, in the same way that the temperature in a field becomes uniform in a thermal diffusion phenomenon. The proposed scheme creates replicas of files in peers probabilistically, where the probability is controlled by using parameters that can be used to find the trade-off between storage load balancing and search performance in unstructured P2P file sharing networks. First, we show through theoretical analysis that the statistical behavior of the storage load balancing controlled by the proposed scheme has an analogy with the thermal diffusion phenomenon. We then show through simulation that the proposed scheme not only has superior performance with respect to balancing the storage load among peers (the primary objective of the present proposal) but also allows the performance trade-off to be widely found. Finally, we qualitatively discuss a guideline for setting the parameter values in order to widely find the performance trade-off from the simulation results.