In this work a numerical procedure for the simulation of the construction process of Roller Compacted Concrete (RCC) dams is described. The basis of the work is a coupled thermos-chemo-mechanical model for the behaviour of concrete at early ages that allows to simulate the observed phenomena of hydration, aging, creep and damage. In this first part only the thermochemical aspects of the simulation of the construction process are presented. The proposed procedure can accurately predict the evolution in time of the hydration degree and the hydration heat production. This allows to obtain the temperature field inside the dam at any time during the construction and the following years. The evolution of the compressive and tensile strengths and elastic moduli can also be predicted in terms of the evolutions of the hydration degree and the temperature conditions. Results from 2d and simplified vertical 1D models are compared and several parametric studies are carried out. The simulation and discussion of the mechanical aspects of the construction process are relegated to a companion paper that follows.