The objective of this research was to develop a building thermal analysis and air quality predictive (BTA-AQP) model to predict ventilation rate, indoor temperature, and long-term air quality (NH3, H2S, and CO2 concentrations and emissions) for swine deep-pit buildings. This article, part I of II, presents a lumped capacitance model (BTA model) to predict the transient behavior of ventilation rate and indoor air temperature according to the thermo-physical properties of a typical swine building, setpoint temperature scheme, fan staging scheme, transient outside temperature, and the heat fluxes from pigs and supplemental heaters. The obtained ventilation rate and resulting indoor air temperature, combined with animal growth cycle, in-house manure storage level, and typical meteorological year (TMY3) data, were used as inputs to the air quality predictive model (part II) based on the generalized regression neural network (GRNN-AQP model), which was presented in an earlier article. The statistical results indicated that the performance of the BTA model for predicting ventilation rate and indoor air temperature was very good in terms of low mean absolute error, a coefficient of mass residual values equal to 0, an index of agreement value close to 1, and Nash-Sutcliffe model efficiency values higher than 0.65. Graphical presentations of predicted vs. actual ventilation rate and indoor temperature are provided to demonstrate that the BTA model was able to accurately estimate indoor climate and therefore could be used as input for the GRNN-AQP model discussed in part II of this research.