The child, Daniel Hedley, was not born at the time of the accident in 1990 and his father Gerald was unaware that his wife, Lynda Woodroffe, was pregnant at the time.
A novice climber, Mr Hedley, 41, was killed after plunging from the north face of the Tour Ronde, near Chamonix in the Mont Blanc range.
Kieran Coonan QC, who is representing Daniel, claims that the fatal fall was caused by the failure of mountain guide, David Cuthbertson, who was also a family friend, to anchor Mr Hedley securely to the mountain.
Mr Coonan described how the pair set out from a mountain hut at 4,000m to climb a 350m section of ice and rock. At first Mr Hedley led but when he complained of fatigue Mr Cuthbertson, an experienced mountaineer, took over.
The court heard that the guide, who is from Dores, Inverness, was 20m above his charge when the ground slipped from beneath him.
The fall caused Mr Hedley's single ice screw, which was meant to attach him safely to the rock face in the event of a fall, to fail and both men plummeted to the snow and rocks below.
Mr Hedley, a respected art conservation expert who had worked at the Courtauld Institute of Art in London and had been working on a book for the Getty Institute in the United States, died from his injuries while Mr Cuthbertson sustained a fracture to his knee.
Mr Cuthbertson, 49, told the court that he had made a conscious decision to disregard strict safety rules, which would have required him to attach Mr Hedley with two anchors, because global warming made the heat so intense that he feared an immediate rock fall.
"It was the hottest I had ever known it even though it was only 8.30 in the morning," the guide told Mr Justice Dyson. "The sun was shining directly on the summit above where we were climbing and I was extremely concerned about the danger of rocks.
"Since the 1960s, global warming has affected the Alps badly. They are far more treacherous now."
Earlier he had explained: "I wanted to move away as quickly as possible to the safety of a rock face to avoid a possible catastrophe of a rock fall from above. Gerry Hedley was my friend. I regret the incident but I still believe I took the right action to get us both out of the way."
Mr Cuthbertson's testimony prompted Mr Justice Dyson to respond: "The sun is at the heart of this defence."
Later the victim's wife, Lynda Woodroffe, told of her plans to meet her husband the following day and tell about her pregnancy.
Six-year-old Daniel Hedley is claiming around pounds 100,000 of damages from the mountaineer for the loss of his father which, he alleges, was caused by Mr Cuthbertson adopting dangerous climbing practices.
Mr Cuthbertson is believed to be the first mountain guide to be sued for negligence in relation to a fatal climbing accident. The ruling could have serious repercussions for organisers and guides involved in dangerous sports and activities.Reuse content