The dogs were found dead in a parked police car outside the force's headquarters on Tuesday afternoon.
Today it emerged the dogs were donated to carry out police work, including tracking down criminals and providing security at major events in the county.
Unlike other police forces which have their own breeding programmes, Nottinghamshire relies on dog breeders putting forward dogs for public service.
The Dogs Trust, the UK's largest dog welfare charity, said it was "saddened" by the news.
A spokeswoman said: "Whilst the cause of death is still to be determined, the charity would like to remind dog owners and police dog handlers that leaving your dog locked in a car can prove fatal, particularly during a heat wave.
"It can take just 20 minutes for a dog to die and temperatures reach over 40 degrees in some vehicles."
The Royal Society for the Prevention of Cruelty to Animals said it was now investigating the incident.
A spokesman for the charity said: "It was reported to us yesterday by Nottinghamshire Police. We are investigating and they are co-operating with us.
"I am sure this isn't the first incident and it won't be the last."
A statement from Nottinghamshire Police said the welfare of its animals was "of paramount importance".
It added: "We endeavour to take every measure possible to ensure their well-being and safety."
It takes nine weeks of intensive training and costs more than £7,000 before a police dog can go out on patrol.
The maximum sentence for causing unnecessary suffering to an animal is six months in prison and a £20,000 fine.
Nottinghamshire Police said the handler had not been suspended.
Peter Davies, the force's assistant chief constable, said: "This is a tragic incident and we value the important work our police dogs carry out on a daily basis.
"That is why we swiftly reported this incident to the RSPCA and we will be working with them very closely."
It is believed the dogs' handler was not on duty at the time and had called in to the force's headquarters at Sherwood Lodge, leaving the dogs to over-heat in the parked car.
It is not known how long they were left in the car but temperatures in Nottingham yesterday hit 29.4 degrees Celsius.
The Independent Police Complaints Commission said it had received a referral from the force and was deciding whether to investigate.
The Dogs Trust also issued advice today to dog owners following the deaths.
The charity advised owners to walk their dogs in the morning and evening when the weather is cooler, making sure they have access to shady spots and drinking water.
It said very hairy dogs should have their fur clipped and owners should be aware that older and overweight dogs are more prone to overheat.
Dogs can also suffer sunburn so owners should apply canine sun cream to their ears, nose and belly, but avoid using human sun cream which can be toxic to dogs.
If a dog shows signs of distress - such as excessive panting, blueness of the tongue or collapsing - the charity told owners to contact their local vet immediately.
In emergencies, dogs should be soaked with water, fanned with cool air and rushed to a vet.
Elaine Pendlebury, senior veterinary surgeon at the PDSA said: "Over the years I have seen countless cases of heatstroke in pets.
"We always tend to think of dogs in cars, which of course can be lethal as recent tragic events have proved, but heatstroke can affect all sorts of animals and is always distressing.
"As we know a car is a death trap in hot weather as it can rise to unbearable temperatures very quickly.
"Never leave a dog in a car, even if you only intend to be away for a few moments.
"You never know what might delay you."
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