Pecorino cheeses were produced using two different manufacturing procedures (either from raw milk or from milk previously subject to a thermisation at 65 °C for 10 s with the addition of starter culture) using the milk obtained from three groups of ewes fed three different concentrates: (1) control, (2) control enriched with 100 g/kg of extruded linseed, and (3) control enriched with 200 g/kg of extruded linseed. All concentrates were administered with alfalfa hay ad libitum. The extruded linseed-enriched diets increased the concentration of n-3 fatty acids, conjugated linoleic acid, and monounsaturated and polyunsaturated acids in raw milk and thermised milk cheese and decreased the concentration of saturated fatty acids. Changes in the manufacturing procedure did not influence the fatty acid composition of the cheeses but markedly influenced their sensory properties. In particular, heat-treating the milk and adding a starter reduced the differences in cheese odour, flavour and toughness induced by the diet when raw milk was used. Cheeses made with thermised milk and the addition of starter culture were more uniform and obtained a higher score in the preference test compared with the corresponding raw milk cheeses. An appropriate manufacturing process, therefore, can be a possible strategy to obtain cheeses with improved health-promoting properties and an unaltered acceptance level by consumers.