It was the second fire his Renault has suffered this season as the German driver also had to leap from his car during practice for the Spanish Grand Prix in May.
On this occasion Heidfeld was delayed in his second pit stop at the Hungaroring by a wheel-nut issue, apparently resulting in the car's forward-facing exhausts overheating.
As Heidfeld pulled out of his pit box and onto the pit lane, smoke billowed from the back of the car before it eventually set ablaze.
Pulling onto the grass verge on the main straight, Heidfeld had to quickly jump from his stricken car as flames lapped around him.
"At Barcelona I looked left [in his mirror], saw a small fire and had time to stop," said Heidfeld.
"This one, I looked straight, saw the fire and it got hot. I really felt the temperature. It was scary, much more than Barcelona.
"It's now my second consecutive weekend without finishing, so I'm very disappointed. The last couple of races have not been what I hoped for."
Heidfeld, who crashed out in last week's German Grand Prix, has revealed the team are looking into the exact cause of the fire.
"The stop was a bit longer, which might be one of the reasons, but it is not like the stop was very long," added Heidfeld.
"It was not that I was stationary for 20 seconds or something, but we are still investigating."