According to the Financial Times, Ovo Energy last week emailed customers a list of 10 “simple and cost-effective ways to keep warm this winter”.
As well as cuddling pets for warmth, other tips included “challenging the kids to a hula hoop competition”, “doing star jumps”, and “cleaning the house”.
It came as Britain’s cost-of-living crisis is expected to worsen.
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According to some predictions, energy bills could rise by more than 50% in April for millions of households that are on a standard tariff.
Bristol North West MP and chairman of the Business Select Committee Darren Jones branded Ovo Energy’s tips “offensive” and called on the company to apologise.
In a subsequent tweet, he wrote: “I’m not sure who signed off a marketing campaign telling people to wear a jumper and eat porridge instead of turning on the heating if you can’t afford it.”
Ovo has since apologised for the tips, telling the FT: “We understand how difficult the situation will be for many of our customers this year.
“We are working hard to find meaningful solutions as we approach this energy crisis, and we recognise that the content of this blog was poorly judged and unhelpful. We are embarrassed and sincerely apologise.”
In April, the price cap, which limits the amounts energy suppliers can charge, will rise.
It is already at a record £1,277, but analysts at Investec think it could go up to £1,995.
The increases are due to a major spike in global gas prices, which have been pushed up by high demand around the world.
Meanwhile, bills could be cut by a further £190 by bringing forward proposals on removing policy costs.
Earlier this month, Downing Street suggested that there are not any imminent plans to help keep energy prices down for customers, as households face a potentially crippling price rise in less than three months.