Cpl James Dunsby, from the Wiltshire Territorial Army, and two other reservists, died after SAS selection training in Powys.
The 31-year-old collapsed on 13 July during the training in the Brecon Beacons but died two weeks later.
The funeral service was held with full military honours at St James Church in Trowbridge.
'Scholar and gentleman'
Cpl Dunsby was a reserve soldier serving with the Royal Yeomanry, a cavalry regiment based in Swindon.
He served with the regiment in Afghanistan, alongside Prince Harry.
Another colleague who served alongside Cpl Dunsby described him as “a scholar and a quintessential English gentleman”.
The three men were on a 40-mile (64km) hike when temperatures reached 29.5C (85F).
The other two men were L/Cpl Craig Roberts, 24, from Penrhyn Bay, Conwy, and Edward Maher, 31.
Cpl Dunsby, who grew up in Tasmania, was employed with the Ministry of Defence in Bath and was an analyst in human geography.
He was also a visiting fellow at Pembroke College, Oxford and a member of the Bradford-on-Avon rowing club.
Another colleague has said of Cpl Dunsby: “He touched so many and achieved so much that James leaves this place triumphant”.