The heat of hydration of hydraulic cements results from the complex sets of phase dissolution and precipitation activity accompanying the addition of water to a cement. Heat of hydration is currently measured in one of two ways: 1) through an acid dissolution of the raw cement and a hydrated cement after seven days, or 2) isothermal calorimetry. In principal, the heat of hydration should be predictable from knowledge of the cement composition, and perhaps some measure of the cement fineness or total surface area. The improved mineralogical estimates provided by quantitative X-ray powder diffraction, together with improved statistical data exploration techniques that examine nonlinear combinations of candidate model constituents, are used to explore alternative predictive models for 7-day heat of hydration (HOH7). An All Possible Alternating Conditional Expectations (APACE) exploratory tool, created by combining All Possible Subsets Regression with Alternating Conditional Expectation (ACE), is used to determine which variables within an explanatory variable class and which subsets of variables across explanatory variable classes exhibit the highest potential predictive power for additive nonlinear models for HOH7. While a single, strong model for HOH7 did not emerge from these analyses, some general conclusions did result. Good fitting models include a key structural mineralogical phase (belite preferred), a calcium sulfate phase (bassanite preferred), a total fineness or surface area component (Blaine fineness preferred), and ferrite in conjunction with Fe2O3, or aluminate, or cubic aluminate.