Brown adipose tissue (BAT) is mainly present in young mammals and is important for maintaining body temperature in neonatal mammals because of its ability to produce non-shivering thermogenesis. There is usually a large amount of BAT around the kidneys of newborn kids, but the BAT gradually “whiting” after birth. Screening and validating appropriate reference genes is a prerequisite for further studying the mechanism of goat brown adipose tissue “whiting” during the early stages. In this study, the expression stability of 17 candidate reference genes: 12 COPS8, SAP18, IGF2R, PARL, SNRNP200, ACTG1, CLTA, GANAB, GABARAP, PCBP2, CTSB, and CD151) selected based on previous transcriptome data as new candidate reference genes, 3 (PFDN5, CTNNB1, and EIF3M) recommended in previous studies, and 2 traditional reference genes (ACTB and GAPDH) was evaluated. Real-time quantitative PCR (RT-qPCR) technology was used to detect the expression level of candidate reference genes during goat BAT “whiting”. Four algorithms: Normfinder, geNorm, ΔCt method, and BestKeeper, and two comprehensive algorithms: ComprFinder and RefFinder, were used to analyze the stability of each candidate reference genes. GABARAP, CLTA, GAPDH, and ACTB were identified as the most stable reference genes, while CTNNB1, CTSB, and EIF3M were the least stable. Moreover, two randomly selected target genes IDH2 and RBP4, were effectively normalized using the selected most stable reference genes. These findings collectively suggest that GABARAP, CLTA, GAPDH, and ACTB are relatively stable reference genes that can potentially be used for the development of perirenal fat in goats.