Thieves stole a £200 baby tortoise from a pet shop in Worcester Park on Saturday.
The owners are concerned about the Hermann tortoise, which needs a specially heated cabinet, ideally a purpose-built vivarium with UV lights, to stay awake and grow.
It was in its own glass display cabinet when thieves forced open a panel around 2.30pm.
If it goes into hibernation it is unlikely to survive, says Ian Veal, one of the owners of Pets Place in Central Road.
"The tortoise needs to be looked after carefully or it will die," said Mr Veal. "I am more angry than upset at the theft; that anyone can stoop so low."
Police are looking for four white youths in connection with the theft - two boys and two girls, aged 13-16, who were seen in the shop at the time.
One of the boys was about 5ft 2in tall and wore a dark hooded top. The other boy was slim with spiky blond hair and was 5ft 6in.
One of the girls was of medium build, 5ft 2in tall, with brown, bushy, curly hair. She wore a light coloured hooded top and blue jeans. There is no description of the other girl.
The shop had the beige coloured tortoise, which was captive bred in the UK, for just a couple of weeks.
The 18-24 months old, micro-chipped tortoise fits in the palm of a hand and is too young to generate heat itself.
It also requires a special juvenile diet and vitamins as well as the usual vegetation and fruit food.
Witnesses or anyone with information should contact Worcester Park Safer Neighbourhoods Team on 020 8649 3590, email email@example.com or call Crimestoppers anonymously on 0800 555 111.