Our inner body is protected by the wall of skin to avoid the entry of novel coronavirus and using a shared mercury thermometer even by an infected patient is not likely to be affected by the virus.
The virus is mainly spread through droplet discharged by patients or close contact with them. A shared mercury thermometer may carry the virus if it comes into contact with hands of infected patients or if they leave their droplets on it. The shared thermometer used in hospitals and other public health institutes are disinfected after one use to kill the virus.
Do remember to wash hands carefully and avoid touching eyes, nose and mouth with uncleaned hands as the virus may enter your body through these mucosal tissue. Give special protection to broken skin to prevent the virus from entering from the broken parts.