Rosco, a French Bulldog, was stolen from a garden in Grasmere Avenue, Intake, on Friday after a van pulled up outside and a man grabbed the dog from under a fence.
GRAPHIC CONTENT: Family ducks killed in Sheffield suburbHe jumped into the passenger seat of the van with the dog in his arms and a getaway driver sped off from the scene.
APPEAL: Police hunt continues for Sheffield man wanted over murderThe theft was captured on a CCTV camera and footage has gone viral online, having been shared tens of thousands of times on social media networks.
CRIME: Porsche stolen after house burglary in SheffieldRosco's owners Liam and Kayleigh Cross turned detective over the weekend after finding CCTV footage of the van in the Intake area on the day of the theft and establishing its number plate.
They trawled the streets of Doncaster looking for their pub and spent hours advertising the theft online to make Rosco 'too hot to handle'.
The couple have checked CCTV cameras in and around Intake to try to piece together the movements of those involved in the theft and a police investigation is also under way.
Kayleigh, a mum-of-six, said she is desperate to find Rosco.
She said all her children are heartbroken but one of her sons, who is suspected of being autistic, is particularly affected.
"We are all devastated but one of my children, who is going through the process of being assessed for autism, is really badly affected as Rosco really calms him down," she said.
"He has been waking up two or three times a night to see if we have got him back and he is really upset."
Rosco was in the family's garden with their other dog - a Shar Pei - when he was snatched.
Kayleigh said: "Our garden has a metal fence all around but whoever took it lifted it up at the bottom and grabbed Rosco from underneath it and jumped into the van with him.
"My partner has been all over Intake checking CCTV cameras. He has been driving around all weekend and we have shared Rosco's details on hundreds of websites about missing dogs all over the country.
"We just want to do everything possible to try to get her back because it is like losing a child. Your pets are not just animals, they are part of your family and until someone steals yours you don't appreciate how heartbreaking it is.
"I won't give up until we find him and bring him home. He has to be somewhere, someone has to know something. Please make my puppy too hot to handle."
Anyone with information should call Kayleigh on 07719 576357 or South Yorkshire Police on 101.