if it comes straight down to it. and you find insulation.
go grab a couple rolls of heavy duty foil (grocery store / dollar store) used for cooking, and goto a local hardware store and pickup some spray on / tac glue. and run some foil over it all. it can help reflect radiant heat. the insulation that comes with foil backing, just professionally installed kitchen foil (most likely thinner) due to professional made. that is just fine, just a reflective surface metal surface.
you can pickup "electrical spray foam" at most local hardware stores, most likely in the painting section. were other spray foams are located. it more likely rated at a higher temperature,
hard board insulation (tends to come in 8'x4' feet sheets) and can come in one or both sides with foil. grab some hvac metal/foil tape. and go at it.
in the plumbing -> pipe insulation area -> you can normally find larger strips of a rubberish roll of pipe insulation. (large width weather strips in thought). with a glue backing on them.
you might find some fiberglass with foil backing some place. that is more workable like a towel you use to dry off after a shower as in workable. you might find it in plumbing pipe isle, or in insulation section for insulating homes walls and attics at large local hardware stores.
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i have used hard board insulation nails with the large plastic washers, i removed the nails, and then inserted screws, or a rivet into the plastic washer. to hold insulation before.
if you go with spray foam, let the foam fully cure (say a week), then go back and trim it up with a razor knife, dremal and various sanding discs and drums for it. to even wire brush wheel.
if you get an electrical "hot knife" used for cutting up hard board insulation. they can really go at work. ((make sure you are outside or in a well ventlated area)), until you figure out how fast you need to go and how how the blade stays warm as you cut. other wise lots of nasty fumes come off. have some sort of junk 2x4 or something. to slide both sides of blade against, to help wipe off any sort of gunk that can build up on the knife.
myself, tend to use hardboard insulation, rough cut it, and make it a little loose to easily fit it in. mark spots for screws and like, and then run a bead of spray foam around it all, toss hardboard insulation up, run some sort of screws/nails/etc.. to hold in place, then foil tape it all up. ((doings for a metal shed, small cabin, etc. on farm)).
--the nails/screws are needed to hold hard board insulation in place, so spray foam does not pop the hard board out of position.
--the foil tape is to help close up any spots were air may come in/got out. but also to help keep the spray foam in check. so it does not come out as it sets up / cures. so i do not have to go back and do a bunch of work cleaning up the spray foam.
--i tend to go through a lot of paper towels, (pockets end up full of single sheets stuff into them), so i can grab a sheet easily even with sticky messy fingers, and use as needed.
--if you get spray foam on something, let it cure and harden for a day or so. then come back and pop it off. if it is still wet. do not touch it. you will only make a bigger mess.
--i tend to always use "great stuff (closed cell) in red can" and rarely ever use open cell spray foam.
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being a sheet metal machine... and if you do not want to mess with rivits. might suggest bolts/nuts. with rubber washer.
bolt on outside, rubber washer, sheet metal of unit, insulation, metal or plastic washer, nut. the rubber washer on outside is were you want the water tight seal to be.
you might find a box of screws/nails for metal siding, or for metal pole barns screws/nails for attaching the metal. generally come with rubber washers on them to create a water tight seal.
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EDIT, you might want to find some fabric. or cheapest thinnest piece of carpet you can find. and tack up . both to help with sound, but also so you do no end up getting cooked from the inside out, as sun reflects off of foil.
there is more expensive "sound proofing material" that might also act like an insulation. vs using spray foam and hard board insulation and like.
tack up as in. spray glue, carpet metal edge runners along walls. to hold carpet in place. some of the carpets holders, act ore like a "large clamp" or metal brake. in how they hold onto carpet/fabric.
