To estimate the heat flowing into the workpiece in machining processes, an inverse algorithm based on the Conjugate Gradient Method (CGM) is proposed to estimate the unknown boundary heat flux. Outgoing from infrared temperature measurements the heat flowing into the work-piece for an orthogonal cut can be estimated. To increase convergence of the estimated solution, a sensitivity analysis of the direct problem is performed to determine the identifiability of the boundary heat flux on the measurement site. The proposed Fixed Identifiability Conjugate Gradient Method (FIX-CGM) computes a step size function considering the identifiability of the unknown boundary condition to minimize the objective function. In contrast, the CGM computes a scalar step size by integrating the difference between measured and calculated temperature over time. Results show that applying the FIX-CGM for a benchmark case with a step heat flux faster convergence, better accuracy and less sensitivity to noise are achieved.