L/Cpl Craig Roberts, 24, from Penrhyn Bay, Conwy, collapsed and died on 13 July with Edward Maher, 31.
His commanding officer praised a “talented young man” before the service at Holy Trinity Church in Llandudno.
A coroner has also opened an investigation into the death of Cpl James Dunsby, 31, who also collapsed on the day and died on 30 July.
The men were on a 40-mile (64km) hike in the Brecon Beacons when temperatures reached 29.5C (85F).
They had been taking part in a four-week trial for the SAS reservists ending in the hike across the beacons.
They were among six men rescued after collapsing in the hot weather.
L/Cpl Roberts was pronounced dead on the beacons on 13 July at 17:15 BST. Almost three hours later, Mr Maher died at Prince Charles Hospital in Merthyr Tydfil.
L/Cpl Roberts had served with the Territorial Army for more than five years and was a member of the 3rd Battalion Royal Anglian Regiment. He is understood to have served in Afghanistan and Iraq as a reservist.
He had worked as a teaching assistant in London and was due to take up a job in Whitehall in the office of Education Secretary Michael Gove.
Lt/Col Paul Morris, commanding officer of the 3rd Battalion, the Royal Anglian Regiment, paid tribute to L/Cpl Roberts before the funeral began.
“Craig was a talented young man with a bright future ahead of him, both as an army reservist and in his wider civilian life,” he said.
“Craig will be missed dearly by everyone who knew him – his family, his friends, his colleagues and his comrades in the wider army.
“We will miss him greatly and we will remember him.”
An inquest in Brecon, which was opened and adjourned last month, heard the cause of Mr Roberts's and Mr Maher's deaths remained “unascertained”.
At the hearing Powys coroner Louise Hunt warned that the Ministry of Defence (MoD) could face investigation under the Human Rights Act.
She said “right to life” would play an important part in the inquest.
Ms Hunt reiterated those comments on Thursday at the opening of an investigation into the subsequent death of Cpl Dunsby.
The Defence Secretary Philip Hammond has announced a full inquiry into the deaths.