A common challenge in low temperature instrumentation is adequately heat sinking signal wires between room temperature and devices at base temperature. Using cryostat space for adequate heat sinking typically comes at the cost of complexity or experimental space. As such, it is useful to know how much heat sinking is adequate given the materials, heat sources and cooling capacities involved. We present a differential equation for modeling the heat flowing out of a flat cable along an interval over which it is adhered to an insulating interface which is bound to a metallic heat sinking surface and numerical results for realistic heat sinks in the Kelvin range. We also present a computational method for solving this differential equation.