Infantry soldier Josh Hoole was on a pre-training course in the Brecon Beacons on Tuesday 19 July when he died, according to an Army spokesperson.
He was with the Rifles Regiment and was training for the Platoon Sergeants' Battle Course in Brecon.
The 26-year-old had served two tours of Afghanistan and was due to get married later this year.
According to the Army's website, The Platoon Sergeants' Battle Course (PSBC) is a 'promotion qualifying-course, to Sergeant, for Rifles Platoon Sergeants' and is run in January, April and August each year.
It described the PSBC as 'both mentally and physically demanding' – but students receive the 'highest level of tuition and testing to ensure they are fully prepared for the rigors of command."
Temperatures on Tuesday peaked at just above 30C (86F) in Brecon, according to the Met Office.
His family have described him as "beautiful" and "dedicated" in moving tributes.
Mr Hoole's grandfather John Craig said: "He was a beautiful grandson. He was a dedicated soldier.
"He always wanted to be top dog. He was a superfit boy, he kept very fit."
Most soldiers take part in organised, and sometimes independent, pre-course training which can involve marching long distances carrying weight, and digging trenches.
Captain Doug Beattie, who has taken the course and run pre-courses, said it is a tough course, and needs to be so.
He said: "It needs to be demanding and I don't think there should be any call that it shouldn't be demanding, I don't think anybody would want that.
"But being a demanding exercise does not mean that you do not do your risk assessments and take all precautions so that people don't get injured in doing that.
"We cannot speculate in this case and need to wait and see what the cause was."
The death comes after three soldiers - Lance Corporal Edward Maher, Corporal James Dunsby and Lance Corporal Craig Roberts - from the SAS died in 2013 in the same area.
In March the Health and Safety Executive announced it would issue a so-called Crown Censure to the Ministry of Defence over the 2013 deaths.
It said the MoD had failed to manage risks during the training exercise and added that it had worked since the deaths to ensure lessons were learned and future risks reduced.