Speaking from the family home in Bridge Pa, Cowan's father Monty said he had doubts his son would survive. "He's pretty crook. I don't know if he's going to pull through.
"I don't know what's caused it. I'm just waiting and hoping he is going to pull through. The only thing that is saving his life right now is he is super fit and very strong. His body is all that is pulling him through."
Monty Cowan said "Teira" was the youngest in the family and his three sisters rushed to his bedside at Middlemore Hospital as soon as the family learned of the accident. Since then, information has been limited because there has been no change.
He said the young soldier is in an induced coma. "He's been unconscious since he got there. He hasn't moved or anything. I just wait for phonecalls to see if he has improved."
Cowan's discretion about his role in the army would have served him well in the secretive SAS. His father said he was silent on trips home about what he did. "He doesn't discuss anything with us. He won't even tell us where he goes and what he does." Despite his silence, he did tell his father he "might have a shot" at a spot in the elite unit.
Cowan, who recently returned from serving in Timor-Leste, remained in intensive care last night.
"His condition is causing concern," a hospital spokeswoman said.
Army chief Major General Tim Keating said an inquiry would review whether the selection process needed to change.
Keating, who had passed the same selection process once to qualify as a SAS member, said the inquiry would be a "full examination around the specific officer who was injured and how the injury occurred".
Keating said the selection process had been refined over decades and was "a pretty safe process".
"It's very physically and mentally demanding. Its aim is to push you to your physical and mental limits but not to injure anyone."
He said the selection candidates had set out about 1pm on Wednesday for a task which was part of selection.
He said the group was required to complete an 8km run in uniform while carrying equipment in a load-carrying vest weighing about 10kg.
About 2.20pm, the group were reaching the end of the activity when Cowan stopped and fell to the ground "where he became unconscious", said Keating.
"He received immediate first aid assistance and an army medic commenced treatment within five minutes of his collapse."
He said a medic had followed the group through the activity and was close by to help the fallen soldier.
A former SAS trainer said only 10 per cent of people made it through the rigorous SAS selection process.
"It is 60 per cent mental and 40 per cent physical. They only select people that are tough. It is designed to weed out the dreamers and it does.
"If this individual was not prepared enough, had not done enough training, did not drink enough water, he would have struggled and he would have been so focused on not quitting that he would have pushed himself too far," he said.
In the first day of the selection process, hopefuls faced a 2.4km run, 30 push ups, 66 curl ups, a 5m rope climb then had to climb a 1.8m wall.
They also must complete battle efficiency training which involved running 8km in under one hour and 12 minutes carrying 35kg.
Sports physician Chris Hanna said heat stroke could be life-threatening. "If you are exercising in an environment where you are creating more heat than is escaping from your body your temperature will build up.
"If you are wearing protective clothing and wearing a pack you will build up heat," he said.
He said the body functioned best at 37C and organs stopped functioning properly at more than 42C.
"The body loses its ability to regulate its processes and that can cause swelling in the brain. It is vital to cool the person down as quickly as possible to prevent long term damage."
Last year the SAS changed their policy to allow "motivated and talented" civilians to join. SAS training takes nine months, with advanced navigation, weaponry, medical and demolition skills required to be a member of the unit.
