A method of making a heat-sensitive lithographic printing plate precursor is disclosed which comprises the steps of (i) providing a web of a lithographic support having a hydrophilic surface; (ii) applying on the hydrophilic surface of the web a coating comprising a phenolic resin; (iii) drying the coating by supplying heat to the coated web; (iv) a cooling step wherein the web temperature is reduced at an average cooling rate which is higher than if the web would be kept under ambient conditions but not higher than 30° C./s; and (v) winding the precursor on a core or cutting the precursor into sheets. The cooling step provides a significant improvement of the aging behavior of the precursor. A stable sensitivity is obtained shortly after coating.