The toroidal equilibrium position in the Extrap T1 toroidal Z-pinch is studied by measuring the currents induced in the external octupole field rings. Radial profiles are obtained by an internal magnetic coil array. From the magnetic field, profiles of current density, plasma pressure, safety factor, resistivity and input power density are deduced. A polynomial model is developed to simulate the measured profiles. The classical ion heat conduction losses in Extrap discharges are calculated using this model and compared to the power input. For polynomials matched to magnetic field profiles measured in experiments, these losses are small. By varying the coefficients of the polynomials, a region is found where the power input can balance the classical heat conduction losses at higher values of Theta and beta 0.