Ash agglomeration and slagging are responsible for costly maintenance problems in coal-fired boilers. Boiler design and operation rely on critical ash fusion temperatures defined by geometric criteria that explicitly ignore shrinkage or warping. Reproducibility of ash fusion test (AFT) results is known to be a major problem, given the subjective nature of some criteria used in critical temperature reporting. Decades of faulty predictions based on AFT data underscore the need for an objective measure of the likelihood for agglomeration and slagging as a function of coal ash composition and temperature. Heating microscopes and ash fusibility determinators are AFT instruments that are widely available and readily adapted for optical dilatometry of ash cones through digital image analysis. Optical dilatometry enables the continuous measurement of cone height and face area, and the calculation of changes in cone volume and density as a function of temperature during constant heating. A strong correlation was found between the sintering onset temperatures of two synthetic ash compositions measured through optical dilatometry and their corresponding solidus temperatures predicted through thermophysical modeling. The sintering onset temperatures of synthetic slag cones appears consistent with glass transition temperatures estimated using the Kauzmann-Beaman rule. Cone collapse is highly correlated with softening, hemispherical, and fluid temperatures for ash cones. Rapid changes in solid, liquid, and gas volume fractions near the collapse temperature suggest that a transition from capillary to slurry state may play an important role in triggering collapse. Slag cone collapse is better explained by a decrease in viscosity as a function of temperature in the glass working range. The sintering onset temperature and cone collapse temperature are readily understood through thermophysical modeling based on ash composition and provide two additional critical temperatures in the modeling of coal ash agglomeration and slagging.