A monitoring apparatus for molds includes a control unit connectable to a first and second sensor associable with the mold and configured for emitting respective signals representative of a deformation parameter and temperature parameter of the mold. The control unit, in order to define an alert condition, is configured for: defining a value of a threshold parameter as a function of the temperature of the mold and comparing such value of the deformation parameter with a value of a threshold parameter defined as a function of the temperature of the mold; or normalizing, at a reference temperature, the value of the deformation parameter determined at the temperature of the mold and comparing a value of a threshold parameter, defined at the reference temperature, with the value of the normalized deformation parameter at the same reference temperature. Also forming the object of the present invention is a monitoring method and a data medium.