What to insulate
 

I have a piece of thermal insulation material laying around.
I thought to improve my car's preservation of heat between trips (I drive several times every day) by putting it in the engine bay.
But I wonder whether it's better to insulate underside of the hood or the engine cover.
Any suggestions?

First, it'll depend on the type of insulation you have. What are it's ratings for radiant heat and contact heat? Some insulation can take extremely high radiant heat but only half as much when touching the heat source. An example is the Thermotec blanket in the link below. It can take 2000F radiant but only 300F on contact.

Thermo-Tec : Adhesive Backed Heat Barrier

If it's home insulation be careful, most is only rated for max temps below 200F.

Well, there's no way I'll get the specs, it looks similarly to what is used to insulate windshields in the summer an in the winter. So I guess it's more about radiant heat.

Any chance we could get a picture? Even if it's a google picture of something that looks just like it?

Something like that:
THERMAL EXTERNAL SCREEN BLIND ducato sprinter transit vwt4 vwt5 iveco | eBay

I looked at the edge, it's 1 mm of foam glued to aluminum foil.

Id put that on the under side of the hood and any other exposed metal in the engine bay. An under engine cover will help a lot too.

I'd do the same but first if you have any to spare cut out a bit and stick it to the underside of the hood to see how it handles the heat. It'd probably be better to find out a 1sq inch tab melts or catches fire than have the whole hood burst into flames.

Good point, fiberglass insulation is generally fire retardant but foam not so much.

It might not help much unless you have a grill block and belly pan. Otherwise a slight breeze will cool the engine anyway.

In the summer, even w/out direct sunlight the car would stay warm under the hood for several hours with just a stock partial belly pan.
Now temps are lower and I have a partial grille block, hope to be able to re-use as much heat as I can.
I don't really think that fire will be an issue as I never noticed hood / engine cover to be very hot, but it's definitely worthwhile to waste some material to check even if I'm going to have a hole in insulation because of that; a tiny piece won't make a difference.