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Abstract: This paper presents a sound theoretical formulation and an effective numerical implementation of a heat-flow and hydration model for concrete hardening. The model is based on the Fourier equation of heat flow with the adiabatic hydration curve employed as a reference for simulating the hydration heat source. The proposed formulations are based on a consistent scheme for the partial differential equation and its boundary and starting conditions. The hydration kinetics is simulated through the Arrhenius approach. Formulations for the compressive strength and the elastic modulus are provided and the maturity function is also considered. A finite difference numerical solution is derived with a forward explicit time integration in the time–space domain. The numerical solution is designed as a stepwise “recipe” specifically conceived to be easily implemented by means of either a high-level programming language or even a spreadsheet tool. Experimental temperature measurements for two different mixtures, under adiabatic and semi-adiabatic conditions, are used for validating the proposed model. The adiabatic and semi-adiabatic temperature simulations show good agreement with the experimental data for both concrete mixtures. The degree of hydration could be simulated and used as the fundamental parameter for scrutinising the evolution of the compressive strength. Particularly, a linear trend between the compressive strength and the degree of hydration and the maturity was figured out. [Copyright &y& Elsevier]