Empirical observations and mathematical models show that climate warming can lead to the northern (or, more generally, poleward) spread of host species ranges and their corresponding diseases. Here, we consider an unexpected possibility whereby climate warming facilitates disease spread in the opposite direction to the directional shift in the host species range. To explore this possibility, we consider two host species, both susceptible to a disease, but spatially isolated due to distinct thermal niches, and where prior to climate warming the disease is endemic in the northern species only. Previous theoretical results show that species distributions can lag behind species thermal niches when climate warming occurs. As such, we hypothesize that climate warming may increase the overlap between northern and southern host species ranges, due to the northern species lagging behind its thermal tolerance limit. To test our hypothesis, we simulate climate warming as a reaction-diffusion equation model with a Susceptible-Infected (SI) epidemiological structure, for two competing species with distinct temperature-dependent niches. We show that climate warming, by shifting both species niches northwards, can facilitate the southward spread of disease, due to increased range overlap between the two populations. As our model is general, our findings may apply to viral, bacterial, and prion diseases that do not have thermal tolerance limits and are inextricably linked to their hosts distributions, such as the spread of rabies from arctic to red foxes.