This paper describes our proposed technique AutoDomainMine that performs data mining guided by fundamental knowledge of the domain. The data being mined consists of input conditions from quenching experiments and the resulting heat transfer curves, i.e., plots of heat transfer coefficients versus part temperature. Since heat transfer coefficients characterize quenching, the estimation assists decision-making. This avoids running laboratory experiments which consume considerable time and resources. AutoDomainMine integrates two data mining techniques, clustering and classification, into a learning strategy. It clusters curves resulting from existing experiments and uses decision tree classifiers to learn the clustering criteria, i.e., input conditions characterizing the clusters. The learned criteria are used to design a representative pair of input conditions and heat transfer curve per cluster. The decision trees and representatives serve as the basis for estimation. When input conditions of an unperformed experiment are submitted, the decision tree path is traced to estimate its cluster and hence the corresponding heat transfer curve. Also when a desired heat transfer curve is submitted, it is compared with the representative curves. The input conditions of the closest matching curve are the estimated conditions to achieve the desired curve. AutoDomainMine on evaluation gives accuracy higher than state-of-the-art estimation techniques.