Is it permissible to pour boiling water on a mouse or expose it to the sun until it dies, and are these two methods considered part of the burning that is forbidden by Islamic law?

Mice are among the noxious creatures that may be killed both within and outside the sacred precincts (Ḥaram). However, they should not be killed by means that involve torture by fire, due to the Prophet’s (peace and blessings be upon him) prohibition of torture by fire and his command to be merciful in killing.