In this paper, we used tight-binding model to calculate the thermal properties of tetragonal silicene (T-Si). T-Si has a zero band gap with two Dirac points and linear dispersion around them. When a vertical electric field is applied to the T-Si, the band gap opens up as the strength of the electric field increases. This suggests that T-Si could potentially be used in electronic and optoelectronic devices that require a tunable band gap. Applying a magnetic field leads to split of the density of states (DOS) peaks, which increases in intensity as the strength of the magnetic field increases. The band gap, position and height of each DOS peak are influenced by the magnetic field strength. Due to the dependence of the electronic properties of T-Si on external fields, its thermal properties are significantly affected by external parameters such as electric and magnetic fields and chemical potential. The electric field decreases the thermal conductivity of T-Si and this is attributed to the opening of the band gap, which creates a barrier for charge excitation and reduces the number of available electronic states that can contribute to the thermal transport. The results show that the thermal conductivity of T-Si increases with magnetic field and chemical potential due to the reduction in the band gap and the increase in the charge carrier density. The thermal conductivity in terms of chemical potential (μ), decreases with electric field strength in the presence of the magnetic field. The thermal conductivity (κ(T)) is highest at μ = 0 and decreases as μ increases. The Lorentz number, which relates the electrical conductivity and thermal conductivity, decreases with increasing chemical potential and magnetic field strength, but increases with increasing electric field strength.