A device (1) for cutting labels in a labelling machine, including a cutting roller (2) having at least one blade (3) co-operating with a fixed counter-blade (4) able to be operatively associated to the roller for cutting the labels, a mechanical shaft (5) whereon is keyed said cutting roller (2), a frame (6) to support said mechanical shaft (5) and a heat exchanger circuit containing an operating fluid. Precisely, a first portion (9a) of said circuit is constructed on said support frame (6) and a second portion (9b) of said exchanger circuit is constructed on said mechanical shaft (5), said exchanger circuit thermally interacting with said frame (6) and with said cutting roller (2). The device further includes an impeller for generating a flow of said operating fluid within the heat exchanger circuit, said impeller for generating a flow of said operating fluid being connected to the mechanical shaft (5) and being operatively inserted in said heat exchanger circuit.