During the early postnatal period, lambs have the ability to thermoregulate body temperature via non-shivering thermogenesis through brown adipose tissue (BAT), which soon after birth begins to transform into white adipose tissue. An RNA seq approach was used to characterize the transcriptome of BAT and thyroid tissue in newborn lambs exposed to cold conditions. Fifteen newborn Romney lambs were selected and divided into three groups: group 1 (n = 3) was a control, and groups 2 and 3 (n = 6 each) were kept indoors for two days at an ambient temperature (20–22 °C) or at a cold temperature (4 °C), respectively. Sequencing was performed using a paired-end strategy through the BGISEQ-500 platform, followed by the identification of differentially expressed genes using DESeq2 and an enrichment analysis by g:Profiler. This study provides an in-depth expression network of the main characters involved in the thermogenesis and fat-whitening mechanisms that take place in the newborn lamb. Data revealed no significant differential expression of key thermogenic factors such as uncoupling protein 1, suggesting that the heat production peak under cold exposure might occur so rapidly and in such an immediate way that it may seem undetectable in BAT by day three of life. Moreover, these changes in expression might indicate the start of the whitening process of the adipose tissue, concluding the non-shivering thermogenesis period.