In one aspect the present subject matter is directed to a system for thermally shielding a portion of a shroud assembly for a gas turbine. The system includes a shroud support having a forward wall that includes a front side that is axially spaced from a back side and a radially inner surface that extends axially between the front and back sides. A shroud is mounted to the shroud support. The shroud includes a leading edge portion that extends towards the forward wall of the shroud support and a trailing edge portion that extends towards the aft wall of the shroud support. A radial gap is defined between a top surface of the leading edge portion and the radially inner surface of the forward wall. A thermal shield is disposed along a bottom portion of the forward wall and is oriented to face towards a flow of combustion gases.