A turbine wheel for a gas turbine engine including a compressor impeller and a radial inflow turbine integral to or attached to the compressor impeller is provided. A compressor turbine wheel including features to increase surface area of a surface of the compressor impeller and/or the radial inflow turbine and/or a passage to flow air between the compressor impeller and the radial inflow turbine is further provided. Methods for cooling radial inflow turbines integral to compressor impellers are further provided.