The thermal properties of volcanic rocks are crucial to accurately model heat transfer in volcanoes and in geothermal systems located within volcanic deposits. Here we provide laboratory measurements of thermal conductivity and thermal diffusivity for variably porous andesites from Mt. Ruapehu (New Zealand) and variably altered basaltic-andesites from Merapi volcano (Indonesia) measured at ambient laboratory pressure and temperature using the transient hot-strip method. The specific heat capacity of each sample was then calculated using these measured values and the bulk sample density. Thermal conductivity and thermal diffusivity decrease as a function of increasing porosity, but specific heat capacity does not vary systematically with porosity. For a given porosity, saturation with water increases thermal conductivity and specific heat capacity, but decreases thermal diffusivity. Measurements on samples from Merapi volcano show that, compared to the unaltered samples from Mt. Ruapehu, hydrothermal alteration deceases thermal conductivity and thermal diffusivity, and increases specific heat capacity. We use an effective medium approach to parameterise these data, showing that when the porosity and pore-fluid properties are scaled for, the measured values agree well with theoretical predictions. We find that despite the microstructural complexity of the studied andesites, porosity is the principal parameter dictating their thermal properties. To understand whether the measured changes in thermal properties are sufficient to influence natural processes, we model heat transfer from magma to the surrounding host-rock by solving Fick's second law cast in 1D Cartesian (dyke geometry) and cylindrical (conduit geometry) coordinates. We provide models for different host-rock porosities (0-0.6), different initial magmatic temperatures (800-1200 °C), and different levels of host-rock alteration. Our modelling shows how the cooling of a dyke and conduit is slowed by a higher host-rock porosity and by increased hydrothermal alteration. The thermal properties provided herein can help improve modelling designed to inform on volcanic and geothermal processes.