Under one aspect, a method of processing a material includes heating a region of the material with a first energy source; exciting an acoustic wave in the material; and transmitting the acoustic wave through the heated region, the heated region changing at least one property of the acoustic wave. The method also can include detecting the change in at least one property of the acoustic wave; characterizing a temperature of the material in the heated region based on the detected change in at least one property of the acoustic wave; and comparing the characterized temperature of the material in the heated region to a threshold. The method further can include, based on the characterized temperature of the material in the heated region being less than the threshold or being above the threshold for an insufficient amount of time, modifying a property of the heated region with a second energy source.