The equations for the terminal characteristics of a composite superconductor are formulated taking into account heat transfer to a coolant, interface thermal contact resistance, and the size of the superconductor itself. The nonlinear heat‐transfer characteristics of liquid helium are also taken into account in an approximate manner. The general relationship for stability is derived in terms of dimensionless parameters involving the size and characteristics of the substrate and the superconductor and the heat‐transfer coefficients at the interfaces between the superconductor and the substrate, and between the substrate and the coolant. It is also concluded that if the superconducting strands are smaller than a characteristic size, one would espect that flux jumps should disappear.