It took until the halfway stage for an initial eight-man breakaway to form, finally moving clear of the rest of the riders during the tricky 3.8km-long Suc au May climb.
The group never led by more than a minute and a half but just four were left as the race neared its conclusion, with Frenchman Alex Baudin joining Johannessen and Pidcock.
This is the second stage of this year’s Tour to have been affected by weather, with fans told not to attend the final 40km of stage three near the Spanish-French border because of wildfires in the area.
On Sunday, more than a third of the country was placed under France’s national weather service’s highest level of alert.
The heat led the CPA, the association which represents professional cyclists, to say that race start times must “evolve” to “protect athletes’ health” given the increasing frequency of extreme heatwaves.
Some riders have urged the Tour de France organisers to consider bringing forward start times to allow the hottest times of the day to be avoided.
Before the stage began, 35-year-old Australian Luke Durbridge, who is riding for the 12th time this year, said it was “pretty insanely hot”.
“It does make a difference, we appreciate the change,” Durbridge told AFP.
“Going forward, if the way global warming is going, we probably need to start changing these start times.”
But Tour leader Pogacar had a more drastic solution, saying changing the start times would not help riders avoid the extreme heat.
“It’s a big topic to discuss, but if I could have the power to change it all, I would change all the calendars, and I would not race in July and August in the hot places, and do a completely different calendar,” he said.
