The Royal Society for the Prevention of Cruelty to Animals said it was investigating the incident under animal welfare legislation. The maximum penalty for causing unnecessary distress to an animal is six months' imprisonment or a 20,000 pound ($33,000) fine, or both.
The dogs' police handler was on duty and had gone inside the building. Police did not say how long the dogs were in the car.
"This is a tragic incident and we value the important work our police dogs carry out on a daily basis," Nottinghamshire Police Assistant Chief Constable Peter Davies said in a statement.
The Dogs Trust, an animal welfare charity, said heat can kill dogs in just 20 minutes, and that temperatures inside cars can top 104 F (40 C).
Nottinghamshire Police has about two dozen dogs, used on raids, to sniff out drugs and assist in policing major events.
