SAN JOSE -- Officials on Monday released the identity of four men who recently died of hypothermia-related causes, with three perishing during the bitter cold snap that arrived in the Bay Area last week.

According to the Santa Clara County Sheriff's Office, Daniel Brillhart, 52, was found on Thanksgiving under a bridge at Delmas and Auzerias avenues close to Highway 87 and Interstate 280 near downtown San Jose. Three more men succumbed to the cold on Dec. 4 and 5: Enrique Rubio, 56, in the 600 block of Lincoln Avenue in San Jose; Daniel Moore, 53, at Curtner Avenue and Canoas Gardens near Highway 87 and Almaden Expressway in San Jose; and Andrew Greenleaf, 48, who was found in a garage in the 20000 block of Orchard Road in Saratoga.

Sheriff's officials announced on Friday that the four men were homeless, although Greenleaf has a listed home address where he was found, along with other relatives.

In the wake of the four deaths, 375 additional beds were set up at three emergency cold-weather shelters in Santa Clara County, and they were kept open an extra two hours each morning.

Also, outreach workers from EHC LifeBuilders, other nonprofits, as well as Valley Homeless Healthcare Program staffers fanned out to homeless encampments throughout the county over the weekend. They handed out warm-weather clothing and blankets, and encouraged people to go to the shelters.

In all, they were able to reach about 500 people in encampments and on the streets, said Jenny Niklaus, CEO of EHC LifeBuilders.

Even though temperatures were subfreezing again over the weekend, officials said there were no other deaths due to exposure.

"It's a major win that we didn't lose any more folks to hypothermia," Niklaus said.

Among the people persuaded to come indoors were a man, woman and child believed to be 2 or 3 years old who were in a tent beneath an overpass living near Highway 87 and West San Fernando Street. They came to the cold-weather shelter at the former Sunnyvale National Guard Armory on Saturday night and now are expected to be placed at a family shelter.

As the cold snap is finally expected to ease, the cold-weather shelters will go back to their usual capacity of 275 beds on Tuesday night, Niklaus said.

Elsewhere in the Bay Area, a homeless man was found dead Sunday morning in Hayward, becoming the seventh person in the region to succumb to frigid temperatures over the past two weeks.

The Hayward case came on the heels of the death of another homeless man in the East Bay and an elderly man in his Peninsula trailer over the weekend. Police said cold weather may have been to blame in both cases, although their exact cause of death remains to be seen.

Staff writer Natalie Alund contributed to this report. Contact Eric Kurhi at 408-920-5852. Follow him at Twitter.com/erickurhi.