The invention relates to a package (10) containing a cosmetic product (12), the package comprising a basic body (14), a neck (18) and a closure member or product dispensing member (20) mounted on the neck (18), so as to form an internal volume (16) containing the cosmetic product.According to the invention, the package resists an increase in pressure of at least 0.245 bar within the internal volume (16) together with a rise in the temperature of the product to above 85° C., in particular between 85° C. and 150° C.