The Glasgow Housing Association (GHA) scheme, which gives householders free advice, was launched three years ago.
It is estimated it has so far helped tenants save more than £500,000 on their power bills.
All the big six energy companies announced price increases last autumn, with the average family's dual fuel bill now at a record high of around £1400 a year.
GHA's fuel adviser service offers advice on how to cut bills and get access to the cheapest tariffs.
Advisers can also speak to fuel firms on behalf of tenants and arrange low-cost payment arrangements with energy companies.
James Tarditi, 63, is one of more than 5000 people helped by the scheme since the scheme was launched in 2009.
He had a new meter installed and for 18 months received estimated bills, but was hit with a bill for £900 when the meter was checked.
A GHA fuel adviser contacted his energy company and arranged for the bill to be waived as the meter was faulty.
Mr Tarditi said: "My fuel adviser was brilliant and never took 'no' for an answer.
"It only took a couple of weeks from me contacting GHA to getting this solved.
"I'd say to any tenant who is having problems with their fuel bills to make an appointment with a fuel adviser."
Fanchea Kelly, GHA executive director of housing support services, said: "Rising fuel bills are a big concern for many of our tenants.
"Tenants should be able to put their heating on during a cold spell without the fear of receiving a huge gas or electricity bill.
"The service is free for all of our tenants to use and can make a big difference.
"Tenants can receive expert advice on how to stay warm without hitting them in the pockets."
The fuel adviser service is one way GHA is contributing to Sustainable Glasgow – a partnership which aims to make the city one of the most sustainable in Europe and reduce the city's carbon emissions by 30% by 2020.
Any GHA tenant who would like a visit from a fuel adviser should contact their local housing officer, or phone the customer service department on a landline on 0800 479 7979 or 0141 274 7979 from a mobile.