This paper presents new fully-coupled analytical thermo-poroelastic solutions, introducing four new components to the traditional Local Thermal Non-Equilibrium (LTNE) theory: thermo-osmosis; thermal-filtration; heat sinks due to thermal expansion of the pore fluid and the solid phase; and vertical confinement. Thermo-osmosis, thermal-filtration, and fluid dilation are found to have very different effects in case of LTNE versus local thermal equilibrium (LTE), resulting in a fundamentally different thermo-hydraulic-mechanical (THM) response. The aforementioned non-traditional thermal processes cause generation of notably higher pore pressures in the porous medium that cannot be otherwise predicted using current solutions. Fluid temperatures are more sensitive to these non-traditional thermal processes, compared to the solid phase temperatures. Thermo-osmosis is found to have more significant effects under LTNE compared to LTE, and to be the dominant mechanism affecting solid temperatures, pore pressures and stresses. Thermal-filtration and heat sink due to fluid thermal expansion are the dominant mechanisms affecting fluid temperatures. The vertical confinement and formation anisotropy is shown to notably impact the THM response of a porous layer to heat source or sink. The impact of the aforementioned four novel components are found to be enhanced under an impermeable hydraulic boundary compared to a permeable boundary condition.