Abstract: An ink jet printer with a piezo printing head (19) ejects lactate ink onto an uncoated printing medium (16) within the area of a surface to be imprinted. A preheating area (21) for preheating the printing medium (16) from its side opposing the piezo printing head is connected upstream of the surface to be imprinted, whereby the preheating area (21) can be adjusted to a temperature from 24° C. to 50° C. depending on the type of material and its thickness and/or the transport speed of the printing medium (16). There is an after-heating area (22) for drying the lactate ink applied to the printing medium (16) connected downstream of the surface to be imprinted from the side of the printing medium (16) opposing the piezo printing head (19). The surface to be imprinted is thermally insulated from the preheating area (21) and the after-heating area (22) so it is thermally decoupled from the heating of the preheating area (21) and the after-heating area (22).