One of two servicemen who died during the selection process for the Territorial Army's section of the SAS has been named by the Ministry of Defence (MoD).
Lance Corporal Craig Roberts died during a military exercise in the Brecon Beacons on Saturday when temperatures soared to 29.5C (85.1F).
A second soldier, who has not yet been named, also lost his life, while a third remains in hospital.
In a statement, the MoD said: "It is with great sadness that the Ministry of Defence can confirm the death of L/Cpl Craig Roberts and another Army reserve soldier during a training exercise in the Brecon Beacons at the weekend.
"Our thoughts are with their families and friends at this difficult time.
"The families of the soldiers have requested that their privacy is respected at this difficult time."
It is not expected that the MoD will name the second soldier.
Police and the MoD are investigating the deaths of the men, who were part of a group training in Wales's rugged Brecon Beacons on Saturday.
Sources have said the men were at the start of a period of assessment in the selection process for the Territorial Army's section of the SAS, after completing a period of training and preparation.
The deaths have led to question marks over the way rigorous SAS training is carried out, amid speculation the extreme temperatures caused the men's death, but an MoD spokesman earlier said there are no plans to change "routine exercises" in light of the incident.
Members of all four of South Wales's mountain rescue teams were called out to assist when the two servicemen died.
Thirty members of Central Beacons, Brecon, Western Beacons and Abergavenny-based Longtown Mountain Rescue Teams joined the operation near Pen y Fan, the highest mountain in South Wales.
Phil Speck, who was walking in the Brecon Beacons on Saturday, told the BBC he saw soldiers on exercise, but nothing to suggest the tragedy that would later happen.
Mr Speck, whose own walking party stopped at 2.30pm because of the heat, said they saw soldiers throughout the time he was walking from 10.30am until then.
"They did look very hot, they were tired in the afternoon, but it did kind of seem like you would normally see the soldiers when you're walking up there," he said.
He said he saw a few soldiers resting at some points, and noticed one in particular who was sitting down, but added: "I think maybe if we had walked past another walker who was on their own, you might have gone 'Is everything OK? Do you need some extra water?'
"They looked very hot and sweaty but when you see the soldiers you do walking in the Brecon Beacons, you see them all the time, you kind of get used to the fact they can cope with those conditions."
The Brecon Beacons is one of several locations British military use as part of their training.
Its rugged and sprawling terrain helps prepare soldiers physically and mentally for warfare as well as put their logistic skills to the test, making it an ideal area for elite forces personnel like the SAS, but it can prove dangerous even to the most hardened and physically fit.
Earlier this year Army captain Rob Carnegie was found dead on snow-covered Corn Du mountain. It was thought he had been taking part in a gruelling 17-40 mile march in freezing conditions as part of a selection process for the special forces regiment when he collapsed and died.
An unnamed Army officer earlier told the Daily Mail: "The troops are desperate to prove they are up to joining the SAS and push themselves harder and harder. They are encouraged to by the instructors who are unforgiving.
"There is going to be a huge inquiry into what happened because, on the face of it, these lads look like they've been marched to death.
"More should be done to ensure these needless tragedies don't occur."
According to the MoD website, the SAS (Reserve) selection course is run twice a year and consists of two main components - "aptitude" and "continuation".
The "progressively arduous" aptitude phase is designed to select volunteers with the right qualities, including physical and mental robustness; self confidence; self discipline; the ability to work alone; and the ability to assimilate information and new skills.
According to the website, the continuation training - after passing aptitude - is an intensive period of instruction and assessment on Special Forces tactics, techniques and procedures, including weapons and standard operating procedures.
Matthew Dorrance, mayor of nearby town Brecon, which is home to The Infantry Battle School, said: "It's incredibly sad for the friends and family of the people who have lost their lives and our thoughts are with the person who is injured.
"In one way we've been blessed with the weather but for people working in this heat, they're tough conditions."