The thermal properties of volcanic materials are required for modelling and for understanding volcanic surface heat fluxes and timescales for cooling magma. However, compared to volcanic rocks, there are relatively few thermal property data for unlithified granular volcanic materials. Here, we measured the thermal properties of a suite of hydrothermally altered powders from La Soufrière de Guadeloupe (Eastern Caribbean) as a function of water saturation degree. Our data show, under dry conditions, that thermal conductivity and thermal diffusivity decrease, and that specific heat capacity does not change systematically, as a function of the degree of alteration of the unlithified granular material. For example, thermal conductivity decreases from ~0.3 to ~0.2 W·m−1·K−1 as the quantity of alteration minerals in the samples increases from ~10 to ~70 wt%. We interpret the decrease in thermal conductivity with increasing alteration as the result of the lower thermal conductivity of the alteration mineral assemblage relative to the unaltered assemblage. Our data also show that thermal conductivity increases from ~0.2–0.3 to ~0.8–1.1 W·m−1·K−1 as saturation degree increases from dry to at, or close to, complete saturation, due to the higher thermal conductivity of water compared to air. We show that an empirical model for variably saturated granular media is in general agreement with our data and provides a framework to predict the thermal conductivity of unlithified granular volcanic materials as a function of saturation degree. The data and modelling provided herein can help improve heat flux calculations designed to inform on volcanic and geothermal processes.