Measurement of cardiac output is often investigated using a technique based on hot-film anemometry. Here, we discuss a modification to hot-film anemometry, which involves a cylindrical heating element mounted flush on the surface of a typical Swan-Ganz catheter. In contrast to traditional thermodilution, the method discussed here has the potential to allow continuous monitoring of cardiac output. This paper demonstrates that there is a simple approximate relationship between the power input to the device to maintain a temperature of one degree above blood heat and cardiac output. Since, the heat transfer and the fluid flow decouple, a numerical model of the heat transfer of a cylindrical catheter (with heating element) sitting concentrically within a rigid cylindrical artery is developed. Numerical results were obtained for a wide selection of flow profiles, including experimental data. The results indicate that the cardiac output/power input relationship is extremely robust with respect to flow profile and system parameter variation.