In optically excited 2D phototransistors, charge transport is often affected by photodoping effects. Recently, it was shown that such effects are especially strong and persistent for graphene/h-BN heterostructures, and that they can be used to controllably tune the charge neutrality point of graphene. In this work we investigate how this technique can be extended to h-BN encapsulated monolayer MoSe2 phototransistors at room temperature. By exposing the sample to 785 nm laser excitation we can controllably increase the charge carrier density of the MoSe2 channel by Delta n approximate to 4.45 x 10(12) cm(-2), equivalent to applying a back gate voltage of similar to 60 V. We also evaluate the efficiency of photodoping at different illumination wavelengths, finding that it is strongly correlated with the light absorption by the MoSe2 layer, and maximizes for excitation on-resonance with the A exciton absorption. This indicates that the photodoping process involves optical absorption by the MoSe2 channel, in contrast with the mechanism earlier described for graphene/h-BN heterostroctures.