Thermal and pore-pressure variations induced by the circulation of hydrothermal-magmatic fluids in porous and permeable media contribute to ground deformation in volcanic areas. Here, we use solutions for the calculation of the displacements induced by pore-pressure and temperature changes for simplified geometry sources embedded in an elastic half-space with homogeneous mechanical and porous properties. The analytical solution for a spherical source is reviewed, and a semi-analytical approach for the calculation of the displacement for a cylindrical source is presented. Both models were used for the inversion of the daily deformation data recorded on Vulcano Island (Italy) during the 2021 unrest. Starting from September 2021, Vulcano Island experienced an increase in gas emission, seismic activity, and edifice inflation. The deformation pattern evolution from September until mid-October 2021 is indicative of a spatially stationary source. The modeling of the persistent and continuous edifice inflation suggests a deformation source located below the La Fossa crater at a depth of approximately 800 m from the ground surface undergoing a volume change of approximately 105 m3, linked to the rise in fluids from a deeper magmatic source. Corroborated by other sources of geophysical and geochemical evidence, the modeling results support that thermo-poro-elastic processes are sufficient to explain the observed displacement without necessarily invoking the migration of magma to shallow levels. Our findings demonstrate that thermo-poro-elastic solutions may help interpret ground deformation and gain insights into the evolution of the hydrothermal systems, providing useful implications for hazard assessment during volcanic crises.