A fluid model of magnetospheric convection appropriate for the inner magnetosphere, including the effects of heat flux in collisionless plasma, is presented. The plasma is assumed to be isotropic, with the flow speed much less than the thermal speed, and parallel electric fields and loss cone effects are neglected; the effects of slow time variations of the magnetic field are included. The classical transport coefficients are considered and, except for the collisionless heat flux, shown to be negligible in plasma in the inner magnetosphere. Beginning with three-dimensional two-fluid equations, we derive two-dimensional equations for transport of mass and energy mapped to the magnetospheric equator. The equation of mass transport, derived from the mass conservation equations, is equivalent to those obtained in previous studies [e.g., Peymirat and Fontaine, 1994>. The equation of energy transport contains the effects of collisionless heat conduction that represents the transport of energy in the rest frame of the species and has hitherto been neglected in magnetospheric fluid and MHD models. The energy transport equation is shown to be equivalent to that of Peymirat and Fontaine [1994> if the heat flux is neglected. The two equations are coupled first-order partial differential equations; they can be uncoupled by taking linear combinations. The uncoupled equations show that the effect of the collisionless heat flux is to spread information across the fluid drift paths in a manner quite different from that of fluid flow neglecting heat flux. ¿ 1999 American Geophysical Union