Based on the local thermal non-equilibrium (LTNE) saturated thermoporoelasticity theory, temperature, pore pressure and thermal stresses around a spherical cavity in an infinite fluid saturated porous medium are investigated, subject to convective heating/cooling on its impermeable and fixed boundary. Solutions of LTNE saturated thermo-poroelasticity are obtained by Laplace transform. Numerical analysis is performed to examine the effects of LTNE under convective heating/cooling boundary conditions on temperature, pore pressure and thermal stresses around the cavity. The results show that the LTNE effects become more pronounced when convective heat transfer boundary conditions are used. Thermally induced pore pressure and the magnitude of thermal stresses are significantly higher than the corresponding ones in classical saturated thermo-poroelasticity. This is particularly true under convective heating/cooling boundary conditions with moderate Biot numbers.