Monolayers of transition metal dichalcogenides (TMDCs) demonstrate plenty of unique properties due to the band structure. Symmetry breaking brings second-order susceptibility to meaningful values resulting in the enhancement of corresponding nonlinear effects. Cooling the TMDC films to cryogenic temperatures leads to the emergence of two distinct photoluminescence peaks caused by the exciton and trion formation. These intrinsic excitations are known to enhance second harmonic generation. The nonlinear signal can be greatly increased if these material resonances are boosted by high-quality factor geometric resonance of all-dielectric metasurfaces. Here, we experimentally observe optical second harmonic generation caused by excitons of 2D semiconductor MoSe2 at room and cryogenic temperatures enhanced by spectrally overlapped high-Q resonance of TiO2 nanodisks metasurface. The enhancement reaches two orders of magnitude compared to the case when the resonances are not spectrally overlapped.