Jay Leno might not be out of the woods yet regarding his scary car fire incident ... but the good news is the doctor who's giving him treatment says things should be A-OK for the comedian.
Dr. Peter Grossman of the Grossman Burn Center in West Hills gave the much-anticipated update on Jay ... saying during a press conference Wednesday he's gone through one surgery so far to treat his burns, but has another one scheduled for later this week.
He confirms Jay suffered a mix of deep second and possibly third-degree burns to his face, hands, and chest ... but believes his patient is on his way to making a full recovery.
TMZ broke the story, Jay was seriously burned while working on his 1907 White Steam Car in his Burbank garage over the weekend, fixing a clogged fuel line.
The comedian told us, from his hospital bed, there was a fuel leak -- causing gas to spray on his face and hands. Almost simultaneously a spark triggered an explosion, setting the comedian on fire.
Dr. Grossman adds Jay's a "kind and engaging" patient ... and was even in great spirits recently -- passing out cookies to the kids being treated at the hospital.