The fire in Dumfries was discovered shortly before 10pm on Monday.
Various yellow weather warnings for wind, rain and snow have been put in place from Saturday until Tuesday.
Police said the body was badly decomposed and had 'clearly been in the water for some considerable time'.
A new buyer would become part of "postal history", according to network boss.
A 78-year-old man and his 77-year-old wife were both hurt during the raid.