Recently, there have been several proposals to build low-aspect-ratio or spherical tokamaks with plasma currents in the range of 1 MA. These low-aspect-ratio tokamaks employ conventional engineering, except in the central core, which contains the central toroidal field conductors and an ohmic heating solenoid (if present). To achieve low aspect ratios, these components must be engineered to the limits of stress and thermal properties. Solutions are found for the steady-state cooling of the toroidal field conductors. The solenoid, which must be high performance to produce the flux swing required for a 1-MA plasma current, cannot be cooled steady state. The mathematics and procedures necessary to study these issues are given.