Analysis and design of total temperature probes for accurate measurements in hot, high-speed flows remains a topic of great interest in aerospace propulsion and a number of other engineering areas. Despite an extensive prior literature on the subject, prediction of error sources from convection, conduction and radiation is still an area of great concern. For hot-flow conditions, the probe is normally mounted in a cooled support, leading to substantial axial conduction along the length of the probe. Also, radiation plays a very important role in most hot, high-speed conditions. One can apply detailed computational methods for simultaneous convection, conduction and radiation heat transfer, but such approaches are not suitable for rapid, routine analysis and design studies. So, there is still a place for low-order approximate methods, and that is the subject of this paper. Of course for an approximate method to be useful, it must be convenient and rapid to use, it must be robust and, most importantly, it must include models of the key phenomena with an appropriate level of fidelity. Here, we present an enhanced, low-order model that includes conduction with variable thermal conductivity, convection with varying convection coefficient, varying diameter (and thus area) along the length and radiation, all implemented in a convenient MATLAB code. We have also developed a new and unique computational procedure to integrate the enhanced low-order model with CFD/CHT to accurately predict the important influences of radiation under different conditions in a very efficient manner.