I guess it depends on how sunny it is. I don't know, but that insulation is meant to act as a fire retardant in some cars. In case of an angine fire, the plastic fasteners melt, and drop the insulation. It then, at least partly, smothers the fire.
I doubt the risk would keep me from removing the insulation, if I felt that would help in whatever issue you are having, but it's better knowing all the ramifications of doing something.
90% of the time it's sound insulation. I've seen plenty of cars with it removed for years without bothering the paint. parking it in the sun will bother the paint more. it may reduce underhood temps a little but once the engines running, there's enough airflow it won't bother it much.
1991 Toyota Pickup 22R-E 2.4 I4/5 speed
1990 Toyota Cressida 7M-GE 3.0 I6/5-speed manual
mechanic, carpenter, stagehand, rigger, and know-it-all smartass
"You don't get to judge me for how I fix what you break"
I've got a large piece of corrugated cardboard from a box covering the top and two sides of my engine to help it maintain temps.
Does it help?? maybe. I live in a 9000 DD climate and will take any advantage when it's -20F. At that temp, the hell with mileage, I just want the heater to warm up!
Is the underside open between the bumper and the front of the radiator; that could be blocked. Where is the air intake getting air; warmer air under the hood would warm quicker than a cold air intake from outside the engine bay.