Since the COVID-19 outbreak has started in late 2019, SARS-CoV-2 has been widely detected in human stools and in urban wastewater. No infectious SARS-CoV-2 particles have been detected in raw wastewater until now, but it has been reported occasionally in human stools. This has raised questions on the fate of SARS-CoV-2 during wastewater treatment and notably in its end-product, wastewater treatment sludge, which is classically valorized by land spreading for agricultural amendment. In the present work, we focused on SARS-CoV-2 stability in wastewater treatment sludge, either during storage (4 °C, room temperature) or thermophilic anaerobic digestion (50 °C). Anaerobic digestion is one of the possible processes for sludge valorization. Experiments were conducted in laboratory pilots; SARS-CoV-2 detection was based on RT-quantitative PCR or RT-digital droplet PCR. In addition to SARS-CoV-2, Bovine Coronavirus (BCoV) particles were used as surrogate virus. The RNA from SARS-CoV-2 particles, inactivated or not, was close to the detection limit but stable in wastewater treatment sludge, over the whole duration of the assays at 4 °C (55 days) and at ambient temperature (∼20 °C, 25 days). By contrast, the RNA levels of BCoV and inactivated SARS-CoV-2 particles decreased rapidly during the thermophilic anaerobic digestion of wastewater treatment sludge lasting for 5 days, with final levels that were close to the detection limit. Although the particles’ infectivity was not assessed, these results suggest that thermophilic anaerobic digestion is a suitable process for sludge sanitation, consistent with previous knowledge on other coronaviruses.