The body of Ewen Beaton, 32, from near Beauly, Ross-shire, has not yet been recovered since the tragedy at Loch Gairloch on August 26.
His young sons, five-year-old Ewen Beaton and Jamie Beaton, two, drowned when their canoe overturned during an outing with another family, the Mackays, from Muir of Ord in Inverness-shire.
Their daughter, five-year-old Gracie Mackay, died in Glasgow's Royal Hospital for Sick Children last Monday.
Her funeral will take place tomorrow in Muir of Ord. Her father and eight-year-old sister swam to the shore to raise the alarm.
A statement issued on behalf of the Beaton family yesterday said: "We would like to thank the police, coastguard, RNLI and all the other emergency services who did everything they could for little Ewen and Jamie. We would also like to thank everyone for their tireless efforts in the ongoing search for Ewen, including emergency services, local residents and visitors to Gairloch.
"Our focus remains firmly on finding Ewen and bringing him home."
The Mackays also thanked the emergency services, hospital staff and the continued support of their local community.
They said: "We hope that the emergency teams can find Ewen, and the Beaton family is very much in our thoughts at this time."