Owing to high thermal conductivity, copper-based alloys are used to fabricate heat transfer elements of rocket engines, such as combustion chambers, nozzle liners, and metal gaskets. One such alloy is the Copper-Chromium-Zirconium-Titanium (Cu-Cr-Zr-Ti) alloy, which possesses a good combination of thermal conductivity and strength at high temperatures. Thermomechanical processing is an important step in the realization of the various aforementioned heat transfer elements from this alloy. Hence, it is imperative to understand the hot deformation behavior of the alloy as a function of the process variables such as temperature and strain rate. An attempt is made to study the hot deformation behavior of the Cu-Cr-Zr-Ti alloy by subjecting it to uniaxial hot compression tests in the temperature range of 600°C–800°C and strain rate range of 0.001–10 s−1. The flow stress measurement tests were conducted up to a true strain of 0.5 using a Gleeble 3800 simulator. The nature of the flow curves obtained at the completion of the tests indicated the occurrence of dynamic recrystallization (DRX) at deformation temperatures greater than 700°C and with a strain rate below 1 s−1. The work hardening rate was plotted as a function of effective flow stress to assess the flow softening behavior due to DRX at different deformation conditions. A processing map delineating the stable and unstable regions during hot working is developed and validated by observing the microstructures in the corresponding domains. Optimum processing parameters (temperature of 750°C and strain rate of 0.1–10 s−1) for hot working of the alloy were proposed based on a contour map of efficiency of power dissipation. Two constitutive equations are also established: one using the Hyperbolic sine law as proposed by Sellars and McTegart and the other using Kocks Mecking analysis.