Electron heating within the high-speed portions of three simple stream-stream interaction zones has been studied in order to further our quantitative understanding of heat flux regulation in interplanetary space. The ineraction zones were all characterized by enhanced values of (1) the temperature of the total electron population, Te, as well as the temperatures of the core (Tc) and halo (TH) components, (2) the total heat flux Qe, and (3) the interplanetary potential at 1 AU. The shapes of halo electron velocity distributions measured within the interactions zones were not consistent with conditions assumed for the Spitzer conductivity. Instead, temperature and density variations obeyed a polytropic relation with an index of p=0.45¿0.05. If proton-electron coupling and wave-electron coupling are small, this relation implies a conduction law of the form Qe/(NU) &agr;Te, where N is the density and U is the bulk speed in a corotating coordinate frame. However, a conduction law of the form Qe&agr;Te fits the data better, and many other possibilities are consistent with the observations. Although a polytropic relation is simple, the microscopic physics is not. The data suggest that heat flux is not driven by a temperature gradient, since heat appears to conduct from lower to higher temperatures across the compression zones. This implausible occurrence may be possible in part because of the collisionless nature of the halo electrons which conduct most of the heat and because of the resultant macroscopic potential drop, which provides a one-way barrier to the transport of most of the electron population.