The significance of biomechanical analyses for forensic time since death estimations has recently been demonstrated. Previous biomechanical analyses successfully discriminated post-mortem brain tissue from tissue with a post-mortem interval of at least one day when held at 20 °C. However, the practical utility of such analyses beyond day one at 20 °C was limited. This study investigates the storage, loss, and complex shear modulus of various brain regions in sheep stored at 4 °C in 24-hour intervals over four days post-mortem using rheometry tests. The aim is to identify the critical biomechanical tissue property values to predict post-mortem time and assess the temperature sensitivity of the rheometry method by comparing results to recent findings at 20 °C. Thirty sheep brains were examined, including the frontal lobe, parietal lobe, anterior and posterior deep brain, superior colliculi, pons, medulla, and cerebellum. Rheometry tests were conducted, and receiver operator characteristic analyses were employed to establish cut-off values. At 4 °C storage, all investigated biomechanical properties of the examined brain regions remained stable for at least one day post-mortem. Using cerebellar samples stored at 4 °C, a post-mortem interval of at least two days could be determined with excellent diagnostic ability. Complex shear modulus values below 1435 Pa or storage modulus values below 1313 Pa allowed prediction of two or more days post-mortem. Comparisons between 4 °C and 20 °C revealed brain region-specific results. For instance, the complex shear moduli of the anterior deep brain at 4 °C were significantly higher on all individual testing days when compared to 20 °C. In contrast, the combined medulla and pons samples were similar on each day. Rheometry testing of brain tissue consistently stored at 4 °C since death proved valuable for forensic time since death estimations starting from two days after death.