Wastewater-based epidemiology (WBE) demonstrates potential for COVID-19 community transmission monitoring; however, data on the stability of SARS-CoV-2 RNA in wastewater are needed to interpret WBE results. The decay rates of RNA from SARS-CoV-2 and a potential surrogate, murine hepatitis virus (MHV), were investigated by reverse transcription-quantitative polymerase chain reaction (RT-qPCR) in untreated wastewater, autoclaved wastewater, and dechlorinated tap water stored at 4, 15, 25, and 37 °C. Temperature, followed by matrix type, most greatly influenced SARS-CoV-2 RNA first-order decay rates (
k
). The average
T
90
(time required for 1-log
10
reduction) of SARS-CoV-2 RNA ranged from 8.04 to 27.8 days in untreated wastewater, 5.71 to 43.2 days in autoclaved wastewater, and 9.40 to 58.6 days in tap water. The average
T
90
for RNA of MHV at 4 to 37 °C ranged from 7.44 to 56.6 days in untreated wastewater, 5.58–43.1 days in autoclaved wastewater, and 10.9 to 43.9 days in tap water. There was no statistically significant difference between RNA decay of SARS-CoV-2 and MHV; thus, MHV is suggested as a suitable persistence surrogate. Decay rate constants for all temperatures were comparable across all matrices for both viral RNAs, except in untreated wastewater for SARS-CoV-2, which showed less sensitivity to elevated temperatures. Therefore, SARS-CoV-2 RNA is likely to persist long enough in untreated wastewater to permit reliable detection for WBE application.