Despite the fast and sufficient charge transfer from the MoSe2 (or WSe2) "electrode" to the 1T-TaS2 layer, the electronic excitation of the vdW heterostructure does not lead to the nonthermal CDW transition of 1T-TaS2.  Instead, the TaS2 lattice is heated by carrier-lattice scattering, leading to thermal CDW melting at high ionic temperatures.  The lack of nonthermal melting follows from the fact that the time scale of carrier recombination in 1T-TaS2 is similar to or faster than that of charge transfer. 
THERM