The governor said that anyone who does not want their temperature taken needs to understand that the virus is still a threat.
"It's about going forward and finding a new normal with new behavior and new patterns in the workplace," said Cuomo, who announced the executive order at his daily news briefing.
The governor also outlined Phase 1 guidelines for New York City which on Monday will become the final region in the state to begin reopening.
Cuomo said the state is sending one million masks to the MTA as well as 25,000 gallons of hand sanitizer and 500,000 two-ounce bottles of sanitizer to support increased service on trains and buses.
"The MTA will reopen with disinfected train cars, never heard of before," the governor said. "My house doesn't have disinfected bathrooms but the subway cars are disinfected."
Businesses will be allowed to offer curbside pickup provided that employees and customers wear masks.
In instances where curbside pickup is not practical, customers can order in advance and masks and social distancing will be required in the store when they go to pick up their purchase.
Some construction and manufacturing will be allowed to resume with employers being required to provide masks, hold no large meetings, and employees must wear masks when they cannot keep a distance of six feet.
Cuomo said the dramatic drop in the city's positive test rate was remarkable.
"They were at a high of positive testing at 57%, they're now down to 2%," the governor said. "You want to talk about a turn around, this one, my friends, is going to go into the history book."
With continued positive metrics and health data across the state, the governor also moved up the reopening of houses of worship.
Churches, mosques and temples in regions currently in Phase 2 of the state's reopening can open immediately with up to 25% occupancy and so long as they adhere to social distancing guidelines.
"This does not mean you go to a temple or mosque and sit right next to a person," Cuomo said.
The governor said it is up to faith leaders to figure out how to keep people at a safe distance.
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