The heat flux of an active volcano provides crucial information on volcanic unrest. The hydrothermal activity often responsible for volcanic unrest can be accompanied by an increase in the extent and intensity of hydrothermal alteration, which could influence the thermal properties of the volcanic edifice. Therefore, an understanding of the influence of alteration on the thermal properties of rocks is required to better interpret volcano heat flux data. We provide laboratory measurements of thermal conductivity, thermal diffusivity, and specific heat capacity for variably altered (intermediate to advanced argillic alteration) andesites from La Soufrière de Guadeloupe (Eastern Caribbean). We complement these data with previously published data for altered basaltic-andesites from Merapi (Indonesia) and new data for altered rhyodacites from Chaos Crags (USA). Our data show that thermal conductivity and thermal diffusivity decrease as a function of increasing porosity, whereas the specific heat capacity does not change systematically. Thermal conductivity decreases as a function of alteration (the percentage of secondary minerals) for the rocks from La Soufrière and Merapi (from ~1.6 to ~0.6 W·m−1·K−1 as alteration increases from ~1.5 to >75 wt%), but increases for the rocks from Chaos Crags (from ~1.1 to ~1.5 W·m−1·K−1 as alteration increases from ~6 to ~15 wt%). Although the thermal diffusivity of the rocks from Chaos Crags increases from ~0.65 to ~0.75–0.95 mm2·s−1 as alteration increases from ~6 to ~15 wt%, the thermal diffusivity of the rocks from La Soufrière and Merapi does not appear to be greatly influenced by alteration. The specific heat capacity is not significantly affected by alteration, although there is a slight trend of increasing specific heat capacity with alteration for the rocks from La Soufrière. We conclude that the decrease in thermal conductivity as a function of alteration in the rocks from La Soufrière and Merapi is the result of the low conductivity of the secondary mineral assemblage, and that a combination of the high thermal conductivity of cristobalite and the reduction in porosity as a result of the void-filling mineral precipitation can explain the increase in thermal conductivity in the rocks from Chaos Crags. Calculations show that an increase in alteration of a dome or edifice can result in decreases and increases in heat flow density, depending on the type of alteration. Therefore, alteration-induced changes in the thermal properties of dome or edifice rocks should be considered when interpreting volcano heat flux data. We conclude that it is important not only to monitor the extent and evolution of alteration at active volcanoes, but also the spatial distribution of alteration type.