A heating device for heating a thermally fixable sealing cover disposed over the microplate adjacent the wells, a cooling device for actively cooling the microplate and a controller set up to control activity of the heating and cooling devices in a manner to heat the sealing cover so as to thermally fix it to the microplate and to actively cool the microplate so as to keep a temperature of the samples below a predefined temperature when heating the sealing cover. It further relates to a method for automatically sealing a microplate in which the thermally fusible sealing cover is disposed over the microplate, the sealing cover is heated to thermally fix it to the microplate and the microplate is actively cooled in a manner that a temperature of the liquid reaction mixtures is kept below a predefined temperature when heating the sealing cover.