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If the funds in the account go below an agreed limit, the band kicks in.
It can also work with smart meter Nest to turn down the heating and save energy bills if funds are low.
No bank has yet announced that it will be offering the Interact IoT (Internet of Things) platform to customers but Intelligent Environments lists several British banks as clients for its existing online banking platforms.
Chief executive David Webber told the BBC the idea was about consumer choice.
"This is about reacting to changes in your financial well-being," he said.
"Willpower is great if you've got it - not everybody has."
He dismissed the idea that the concept is too controlling.
"If you get home and decide you can afford for it to be warmer you can turn it back up again," he said of the smart meter's automated "economy mode" for home heating.
The Pavlok wristband "shock" function can also be deactivated, Mr Webber added.
He admitted that it had "frivolity" but said it proved the concept.
Mr Webber said he believes the Internet of Things - the idea of connected devices communicating with each other as well as with their owners - will be a landcape-changing industry.
"I think the Internet of Things will be as transformational as tablets and smartphones were a number of years ago," he said.
"I think the interconnectedness of devices is going to transform the way we think and manage whether it's our cars or the things in our home.
"Perhaps you could use this sort of platform where, if you're running short of money your car slips into economy mode, rather than sport mode," added Mr Webber, who insisted that the platform was secure.
'Road to hell'
However Prof Alan Woodward, a cybersecurity expert from Surrey University, said the more connections which are made between devices, the greater the risk of a security weakness.
"Having a convoluted interaction between systems is almost inevitably going to lead to unintended security flaws," he said.
"I know this type of technology is developed with the best of intentions but the road to hell is paved with them.
"Just because you can connect devices en masse doesn't necessarily mean you should."