On Boston Common Saturday afternoon, as temperatures plunged toward zero, 15 volunteers from St. Agnes Parish in Arlington handed out food, outerwear, and hot chocolate to dozens of homeless people.

“We just try to do the best we can to help those in need,’’ said David Moran, a coordinator for the church’s monthly donation program. “But these are the most important days, because we know if at least one person is looking for help, it’s worth it for us.’’

By noon, about 60 men and women had lined up near Park Street to receive the gifts before heading back onto the streets.

One woman, Michelle Carnazzo-Amoroso of Revere, grabbed socks and food from the church volunteers because she knew the long, cold night would be life-threatening. Still, she refused to go to a shelter. Her plan was to stay moving and active, she said, and eventually find a doorway or alley to shield her from the wind.

“The shelters have no room anyway,’’ said Carnazzo-Amoroso, who was already shivering. “So if I’m going to sleep on the floor, might as well sleep out here.’’

In Boston, falling temperatures could hit a record low, according to Benjamin Sipprell of the National Weather Service in Taunton.

The current record sits at minus-3 degrees, set on Valentine’s Day in 1934. Sunday could hit minus-5 degrees while feeling like 20 to 25 degrees below zero, with the windchill, Sipprell said.

“You want to exercise caution with regards to these sort of conditions,’’ Sipprell said. “The coldest temperatures are right before sunrise [on Sunday morning]. But for those still out and about, you need to dress appropriately.’’

A state windchill warning from the National Weather Service went into effect at 4 p.m. Saturday and will continue through noon Sunday, as strong gusts from the northwest threaten to reach up to 45 miles per hour in hilly areas like Worcester and the Berkshires.

In those Central and Western Massachusetts communities, temperatures were expected to approach minus-35 degrees with windchill late Saturday night into early Sunday morning, according to Sipprell. The record low in Worcester is minus-11 degrees, which was set in 1979.

Without windchill, Sipprellsaid, the temperature in Worcester and western areas is expected to dip to minus-10 to minus-15 degrees on Sunday, before it warms considerably across the state as the week begins.

On Monday, according to the Weather Service, temperatures in Boston will climb into the lower 30s and Tuesday will be even warmer, with a high of about 53 degrees.

Saturday night, like Carnazzo-Amoroso, Terri Ramirez, 53, of El Paso,and Jason Martin, 42, of New Brunswick, planned to sleep outside and wait out the deep freeze.

The married couple, who go by “Ma’’ and “Pa’’ on the streets, said they preferred to stay out of shelters, so they could remain together, be with friends, and tend their heaping mound of possessions, which included extra blankets and food for others.

“What worries me about a shelter is that they’ll throw away our things,’’ said Martin. “We’ll just find a doorway’’ nearby to shelter in.

Myra Ackerman, a program coordinator who runs a 24-hour emergency service for homeless families through FamilyAid Boston, said the cold can present intense challenges for social service agencies.

“Obviously, the ideal is not to be outside,’’ Ackerman said. “Sometimes we have to reserve hotels in advance, just because we want to make sure there is a hotel room out there for a family in case they need it.’’

Utility and transportation authorities made preparations for the cold, though they did not expect significant technical issues like those caused by a snowstorm.

Joe Pesaturo, a spokesman for the MBTA, said personnel will perform extra system checks on all vehicles and inspect the air systems on the train, which control braking, suspension, doors, and other key components. A statement from Keolis, the company that operates the MBTA commuter rail, said officials plan to avoid mechanical problems by keeping equipment running overnight.

At Logan Airport Saturday, officials anticipated no delays in service caused by the cold weather, said Massport spokeswoman Jennifer Mehigan.

Mark Van Dam of the Boston Water and Sewer Commission said the agency had contacted residents who have had frozen pipes in the past two years.

“We reached out to those homeowners and said maybe they should think about letting their water drip, or keep water flowing as an extra precaution,’’ Van Dam said. Either way, he added, problems should be scarce.

“It was 40 degrees a couple days ago,’’ Van Dam said.

JoAnne O’Leary of Eversource, New England’s largest energy provider, encouraged worried families to visit the company’s website on tips to stay safe.

She relayed two of the most simple steps.

“Protect yourself and your house,’’ O’Leary said. “It’s better to be safe than sorry.’’

Globe correspondent Nicole Fleming and Aimee Ortiz of the Globe staff contributed to this report. Astead W. Herndon can be reached at astead.herndon@ globe.com. Follow him on Twitter @AsteadWH.