Relatives of two-year-old Liam Fee said they were devastated at their loss.
His body was discovered at the property in Donald Crescent in the Thornton area of Fife on Saturday evening.
Police said his death is being treated as unexplained and inquiries continue.
His family said: "Liam was a happy-go-lucky little boy.
"He was very much loved. Liam had his whole life ahead of him and we are devastated. We would like to thank our friends for all the teddies and flowers which has provided us with some comfort."
Police, who are not looking for anyone else in connection with the death, have spoken to his mother Rachael, 29, and her partner Nyomi, 26, but are no closer to knowing what happened.
Liam has older twin bothers and the family have a large collection of snakes and rats.