Effects of elongation on the radiation heat transport down a spheroidal cavity, located in a conducting solid with a diffusely reflecting cavity-solid interface, are examined. An effective conductivity lambda(c) and a void radiation conductivity lambda(r) are obtained as a function of cavity eccentricity alpha and surface emissivity epsilon. To facilitate the calculations and produce readily applicable equations, a rigorous variational principle is used. Exact solutions are generated in the neighborhood of the spherical cavity (alpha(2) --> 0) for any epsilon > 0, a long needle-shaped void (alpha(2) --> 1) for any epsilon > 0, and a perfect reflector (epsilon --> 0) for arbitrary elongation (0 less than or equal to alpha(2) less than or equal to 1). significant differences arising from the shape change are observed. The alpha(2) --> 0 edge demonstrates a linear increase in lambda(r) with epsilon. At the opposite edge alpha(2) --> 1 and positive epsilon, lambda(r) is a horizontal line independent of epsilon, much like the long cylinder, whose conductivity is a factor of 32/(9 pi) (=1.13) larger. In the neighborhood of epsilon --> 0, lambda(r) is always zero for any 0 less than or equal to alpha(2) less than or equal to 1. The emissivity slope for epsilon --> 0 starts from unity at alpha(2) = 0 and increases monotonically with elongation to a singularity 3 pi[16(1 --> alpha(2))](-1) as alpha(2) --> 1 for the long needle.