The goal of this work is to predict the tool-chip interface temperature during cryogenic machining and determine the effectiveness of this cooling strategy. Knowledge of the tool-chip interface temperature is needed to conduct process planning: choosing a tool cooling geometry, cutting speed, and cryogen flow rate as well as predicting tool life and achievable material removal rate. A detailed explanation of the analytical heat transfer model is presented, which is a modified form of Loewen and Shaw's orthogonal cutting model, where a thermal resistance network is applied to represent the heat transfer mechanisms in, and out of, the cutting tool. An in-depth discussion of the temperature rise at the tool-chip interface during orthogonal machining of titanium alloy Ti-6Al-4V is presented. The effect of cutting speed, cryogen flow rate and quality, and cooling strategy are explored. The model is used to compare the effect of internal cryogenic cooling with external flood cooling using a water-based metalworking fluid or liquid nitrogen. A sensitivity analysis of the model is conducted and ranks the relative importance of various design parameters. The thermal conductivity of the cutting insert has the greatest influence on the predicted interface temperature. The low boiling temperature and phase change are what make internal cooling of a cutting insert with liquid nitrogen effective at reducing the tool-chip interface temperature. If the heat flowing into the tool, from the tool-chip interface, does not exceed the available latent heat in the cryogen, then this method is more effective than external flood cooling.