Newport Library, on High Street, is offering a warm space every Friday from today) through to March 31.
The initiative will see a space in the library set aside where people can meet in the warm, enjoy a cup of tea, and socialise with others.
People are invited to attend the three-hour sessions from noon until 3pm.
Kirsty Finchett, team leader at the library, said they wanted to do what they could to help people who are struggling.
She said they had also been successful in a bid to Telford & Wrekin Council for funding, which will pay for a sofa for people to relax on, as well as refreshments while they are there.
"We have got the heating on so it is not too big a step to give people a tea and a coffee, a few biscuits, put on some games, maybe some jigsaws, then they can spend a bit longer here and use our heating instead of putting the heating on at home," she said.
"We have a lot of customers who already spend quite a bit of time here so we thought it would be nice to make it a bit more welcoming so people can stay a while and use the space."