Freedom Leisure, which runs leisure centres on behalf of New Forest District Council, said it was closing the facilities over the winter.
It said "difficult decisions" were having to be made and it may need to consider other measures to cut costs.
The closure of saunas and steam rooms at Applemore, Totton, New Milton and Lymington leisure centres will be reviewed in the spring.
"These facilities use a significant amount of energy and closing them even for a short period of time will go a long way towards reducing our overall energy consumption," a Freedom Leisure statement said.
It has already temporarily closed swimming pools in Milton Keynes and Rye, East Sussex due to the energy price crisis.
Last month the trust said its annual energy bill had risen from £8m to £20m.
The BBC is not responsible for the content of external sites.