Countdown has installed temperature checking for workers at distribution centres, its e-store, and its meat and seafood plant, who will be sent home if the reading is high.
First Union says the move will upset workers who would have to pay for their own medical costs even if they are declared fit by their GP.
Union secretary for transport logistics and manufacturing division Jared Abbott said it could result in people being sent home even if they had no medical problem.
It proposed the company gave the employee 24 hours to go to a doctor and seek a medical certificate, and covered the cost in that interim period.
"If they're cleared the company would cover the cost of that. If they are deemed to be sick by a medical practitioner then they would go on to sick leave or other leave entitlements."
Abbott said Countdown rejected that suggestion and went ahead anyway.
"It only encourages people to essentially go back to work without a medical certificate and try their luck on the temperature machine which doesn't resolve the issue that they're supposedly there to be resolving."
Countdown turned down an interview request by RNZ, but in a statement general manager for corporate affairs Kiri Hannifin defended the company's actions.
"These are just one part of a suite of health and safety measures we have put in place to help keep our team and customers safe in response to Covid.
"Given we have 20,000 team members and around three million customers a week, we have done everything we can to ensure our safety response is as high and robust as it can be," the statement said.
"This is something we are incredibly proud of."
Hannifin said staying away from work and visiting a doctor when a person had a high temperature was best practice" during the current outbreak.
Abbott said the union simply wanted the process to be "fair".
"Generally, it's very rare that companies actually send people home because they're sick. Usually, those sick leave situations are used because workers are calling in unable to work," he said.
"We have the opposite situation here where the company, who are not medical practitioners are using a very basic piece of technology that simply takes the temperature of someone to determine whether or not someone's fit to work."