The paper presents a theoretical study for the cooling of polymer samples in an injection molding process. The study is applied for neat polylactic acid (PLA), PlA-talc and PLA-starch composite samples representing specimens for mechanical tests reported in literature. A one dimensional model was developed for the heat transport through the thickness of the sample from the polymer to the cooling agent: air in natural convection and water flowing through cooling channels. The heat of solidification of molten polymer was also considered. The model was solved in the frame of Matlab software. The results obtained consist in the evaluation of the final time required to reaches a temperature of about 60 C in the core of the specimen and the evaluation of the temperature profile along the cooling process. When using cooling air in natural convection the temperature profile shows insignificant space variation, but the duration of cooling is about 6 min. The use of cooling water proved to be more efficient in terms of cooling time is about 15-25s, while the temperature gradient in the thickness of the specimen is quite significant at any moment of time.