A sealing machine and method for sealing a preformed tray (2) with a plastic film (26), the method comprising a cooling step in which, by acting on the outside of the tray (2), heat is removed at least from the bottom wall (3) of the tray (2) while the heated plastic film (26) is applied over the tray (2) and a food product (25), and the sealing machine (1) comprising a supporting element which defines a housing (7) which has a fixed bottom surface (9) suitable for making contact, in use, with the bottom wall (3) of the tray (2), a plurality of ducts (19) which define a flow path (20) for a cooling fluid in the supporting element, and a cooling system (17) configured to cool the cooling fluid bringing it to a temperature equal to or less than 10° C., and preferably equal to or less than 6° C.