Methods to predict bioenergetic responses of homeothermic animals were developed. The methods can predict temperatures (e.g., internal, skin surface, and hair-coat surface), heat fluxes (e.g., internal, skin surface, hair-coat surface, convection, and radiation), metabolic heat flux, respiratory variables (respiration rate, tidal volume, expired air temperature), respiratory heat transfer (evaporation and convection), sweating rate, and cutaneous evaporation. The bioenergetic methods were applied to predict bioenergetic responses of livestock. The two main motivations for predicting bioenergetic responses of livestock are 1) the need to sustainably increase food production by 25-70% up to 2050 and 2) to develop systems to ameliorate the negative effects of heat stress on livestock, which costs more than $3 billion to American farmers every year. Bioenergetic models provide insights about animal thermal stress status and comfort, which can be used for timely interventions and/or to design heat reduction systems for animals. Limitations of existing bioenergetic models are a) lack of providing uncertainty measures for the predictions and b) assumption of steady-state. In this study, the first limitation was addressed by developing an integrated bioenergetic model, which integrates fundamental models (analytical and numerical), machine learning models, bioheat transfer, Monte Carlo optimization method, ensemble learning techniques, energy conservation of biological objects, and bootstrapping. The integrated model was applied to predict bioenergetic responses of piglets. The predicted skin and hair-coat surface temperatures (prediction errors of 3.04% and 2.09%, respectively) are the second most accurate predictions published in the literature. The second limitation was addressed through developing the transmission-line modeling (TLM) method to predict dynamic bioenergetic responses. The TLM formulation was shown to predict temperatures with errors within 2% and 1,550 times faster than analytical solutions (based on the truncation of an infinite series solution). The TLM bioenergetic model was applied to predict dynamic bioenergetic responses of dairy-cows and the predictions of skin surface, and hair-coat surface temperatures were within 5% of the measured values. The strength of the methods developed herein are on proving accurate dynamic predictions of bioenergetic responses as well as on providing uncertainty measures of the predictions.