Sharp leading edges on hypersonic vehicles experience very large heating loads and consequent high temperatures. One strategy for for accommodating these effects is to provide very high effectively thermal conductivity which allows heat to be transferred from the hot leading edge to large cool surfaces for radiation into space. Heat pipes integrated within metallic leading edges provide this function, as well as being easy to manufacture and highly robust compared to other material choices. This paper will examine the feasibility of metallic leading edge heat pipes for hypersonic vehicles in Mach 7 flight. Using temperatures and heat fluxes calculated elsewhere, analytic approximations of the temperature distributions and stresses in a prototypical system are analyzed. The analysis is supplemented and confirmed by finite element calculations. Feasibility of the system is assessed by simple calculations on the operational limits of heat pipes.