The 3-year-old German shepherd was working with a search and rescue team on a day-long exercise when he became parted from his handler in the Totara Creek/Red Creek area at Mt Holdsworth.
An officer in charge of the Wellington police dog section said Wairarapa Constable Mike Wakefield, Thames' handler, was devastated after Thames went missing.
"He was working with the team down a really hard spur and it's unknown how, but he just got separated," Senior Sergeant Mark Davidson told the Wairarapa Times-Age.
Police were researching the viability of attaching global positioning system (GPS) devices to dogs.
The research started a few months ago.
"Police have been researching the use of GPS tracking devices. And we've been looking at a technical and operational best fit for potential use on our dogs," police spokeswoman Kaye Calder said.
She said this issue was being discussed both before and after Thames went missing.
If GPS tracking for dogs was to be introduced, it would potentially involve a device attached to dog collars.
However, Ms Calder said dogs were deployed in "a range of situations" so a decision on the best device was not yet decided.