Hundreds of tenants living in council flats have been without heating since August.
The communal boilers serving tower blocks Nettleton Court and Dudeney Lodge, Brighton, broke down 13 weeks ago.
Residents as old as 97 have had to wrap up with blankets and hot water bottles as winter sets in.
They have had to continue paying their £4.09 weekly heating bills despite the breakdown, amounting to £9,251 over 13 weeks.
Their landlord, Brighton and Hove City Council, has been accused of gross incompetence and failing in its duty of care by not solving the problem quicker.
Ward councillor Jeanne Lepper said: "I have written to the chief executive. It is a sorry saga and a shoddy way to treat residents, many of whom are vulnerable and disabled.
"It has caused an enormous amount of distress. It should have been fixed immediately and I want to know why it wasn't."
Signs were initially put up telling residents the system would be fixed within six weeks. A new boiler serving the 174 flats in Upper Hollingdean Road was finally installed last week but residents say it has broken down several times since.
The city council has offered fan heaters to residents but they say they are still forced to wear layers of clothing to keep warm.
Glynis Shipley, 57, of Dudeney Lodge, set up a temporary soup kitchen in her flat to make sure people had something warm to eat.
She said: "The elderly people are just sitting there crying with the cold. We have been using lots of extra blankets and hot water bottles to do all we can to keep warm.
"The council has issued fan heaters to us but they cost a lot of money to run and wouldn't even warm my big toe."
Hot water has been available by turning on an immersion heater but residents have avoided doing this because it is more expensive.
Rita King, 77, of Dudeney Lodge, said yesterday: "The heating has come back on this morning but how long will it last?
"We only have one boiler now and we had three before, meaning there is no back-up.
"They have said we might get the second boiler by Christmas but I won't hold my breath.
"We are very angry. We have suffered for weeks and we have not had one word of explanation from the council."
Ron Slocombe, chairman of the residents' association, said: "I have had phone calls about the heating morning, noon and night.
"The council has been trying to help us but they can't get a boiler out of nowhere."
Coun Lepper added: "It seems to be fixed one minute and broken the next."
A council spokesman said: "The boiler took a long time to buy as boilers for blocks of flats are a rather specialised item. As with replacing a domestic boiler there are inevitable airlocks in the system. This can prevent heating in individual flats working - even though the boiler itself is working.
"So we're having to send out engineers to individual flats as and when faults occur. People should report faults on freephone 0800 0526 140.
"The chief executive will obviously take Councillor Lepper's complaint seriously and any findings will be available to residents."
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