Cold stress in sheep is usually overlooked, even though the animals’ welfare and productivity are affected by low temperatures. The aim of this research was to find out if and to what extent the temperature inside a sheep barn could be maintained within the range of the thermoneutral zone during winter, primarily to increase feed conversion and to reduce GHG emissions. For this reason, an automation system was installed at a sheep barn in northern Greece, and heat losses from the building were calculated. The biogas potential of the sheep barn waste was examined in the laboratory via the BMP method. The results showed that the installation of an automation system together with a hypothetical biogas heating system could maintain the barn’s temperature in the range of a sheep’s thermoneutral zone during winter for the 94% of the scenarios examined if the total energy of the biogas was utilized, while heating energy that was instantly and continuously used succeeded in 48% of the investigated cases. The surplus of energy produced by biogas could potentially raise the water temperature that animals drink up to 2.9 °C. The absence of cold stress decreases the dry matter intake and the CH4 produced by ruminal fermentation. Moreover, lower GHG emissions are achieved as waste is treated through anaerobic digestion, which would likely be released into the environment if left untreated.