Renneted casein gels, often named cheese curds, are traditionally pre-heated by immersion in water before stretching, which influences cheese functional properties. This work aims to understand the effect of pre-heating (cooking) on extrusion process of cheese curds at 80 and 90 °C in a lab twin-screw, co-rotating extruder, and consequences for composition, microstructure and functional properties of the extrudates. The cooking significantly enhanced curd meltability and oiling-off, resulting in faster extrusion, higher exit temperature and lower specific mechanical energy. Microscopic observations at different length scales, combining confocal laser scanning microscopy and X-ray micro-tomography, showed that cooking caused extensive fat coalescence and cracks in protein matrix, resulting in extrudates with less fibrous structure, lower elasticity and tensile strength. The extrusion process induced significantly increased of calcium bridges in extrudates, which may replace weak water-protein interactions and increase relaxation time of the more mobile water fraction (T2.2). The specific mechanical energy was less influenced by the extrusion temperature in cooked than uncooked curds, likely due to a more extensive oiling-off during extrusion of the cooked curd. In agreement with the microscopic observations, extrudates obtained at 80 °C differ from 90 °C specially regarding fat content respectively 23.8–24.8% and 29.5% (w/w) and fat globule size and distribution, influencing fiber formation. In general curds extruded at 90 °C had higher elasticity and tensile strength, which was related to the well-elongated fat domains. This study provided knowledge about extrusion process of curds generating new ideas to improve cheese processing and design customized cheese products.