"Our efforts are clearly focused on reuniting mother and child and the rest of the family members with the child. That's the immediate focus," Jones said.
It's unclear how long the newborn was outside in the cold, Jones said. Kopp said the baby was in excellent health.
Federal, state and local law enforcement officers had been looking for the baby since early Thursday when his mother discovered him missing from a bassinette at a home in the Town of Beloit, a town of 7,500 people. West Branch, Iowa, is about 180 miles southwest of the town.
A woman who had been staying in the same home as Kayden and his mother left the residence early Thursday morning. The mother reported the baby missing later that morning.
The woman was arrested in Iowa on Thursday on an outstanding warrant from Texas. West Branch Police Chief Mike Horihan said she was taken into custody at another gas station less than a half-mile from where the newborn was found.
Investigators traced the woman's likely route of travel that led through Beloit, Illinois and Iowa, Spoden said. Authorities sent out alerts and asked police to search areas along the route.
The West Branch police chief and other officers had been checking areas along Interstate 80 for the child, Kopp said. Jones said the child's discovery was not part of a "directed" search, meaning they weren't told where to look.
"We're celebrating (the chief) as a hero today," Jones said.
Rock County and federal prosecutors are conferring on what charges to file, if any.
"This investigation," Jones said, "is far from over."
In West Branch, Horihan spoke to reporters at the BP gas station, where yellow police tape kept people away from an area on the side of the business.
"It's unique, let's just say that," Horihan said. "I have been in law enforcement for a while and nothing ever surprises me. But it's very unique and very special and I'm just glad everything seems to be fine.
"The baby seems to be doing just fine," he said.
Associated Press writer Ryan J. Foley in West Branch, Iowa, contributed to this report.