The objective of this investigation was to develop a systematic method for the determination of optimal processing temperatures of drug-polymer mixtures for the development of amorphous solid dispersion (ASD) by melt extrusion. Since melt extrusion is performed at high temperature, it is essential that the processing temperature should be as low as possible to minimize degradation of drug and polymer, and yet the temperature should be high enough that the drug-polymer mixture attains certain viscosity that is extrudable and the drug dissolves in the molten polymer. By using itraconazole (ITZ) and polyvinyl caprolactam-polyvinyl acetate-polyethylene glycol graft co-polymer (Soluplus®, BASF) as, respectively, the model drug and the polymeric carrier, melt viscosities of drug-polymer mixtures with 5, 10, 20 and 30% ITZ were studied as functions of temperature and angular frequency. All these concentrations were below the miscibility limit as it was shown separately by film casting that ITZ was miscible with the polymer up to 40%. Since the angular frequency of a rheometer may not be high enough to simulate the shear rate within an extruder, torque analysis as a function of temperature during melt extrusion of selected drug-polymer mixtures was also conducted. The presence of dissolved ITZ had a plasticizing effect on the polymer used, and an intersection point around 150–155 °C was observed, above which viscosities of drug-polymer mixtures were lower than that of polymer itself. Drug-polymer mixtures with 5 to 30% ITZ were extrudable at 150 °C, and torque analysis showed that the mixture with 20% ITZ can be extruded even at 145 °C. These temperatures were 17 to 22 °C below the melting point of ITZ (167 °C). ITZ dissolved due to the drug-polymer miscibility, the viscosity attained, and the shear rate generated. It was confirmed by PXRD and DSC that the extrudates were amorphous. Viscosity and miscibility of drug-polymer mixtures during melt extrusion were identified as critical factors in determining optimal processing temperature.