What kind of off-gassing does that spray insulation produce? Does your sprayer guy know what you're going to be using it for? Have you read the Material Safety & Data Sheet on the type they're planning to use? How does heat affect the cured foam?

I googled 'spray foam insulation msds' and grabbed the first one I came across. Others may be different. Here are snippets. I don't know what they are, but some of it didn't sound so great to be closed in with.

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RHH Foam Systems
VERSI-FOAM Systems I, 9, 15, 50 and 1.75 pcf Refillable - Standard Component A

SECTION 2 - CHEMICAL COMPOSITION
CHEMICAL.................... CAS #................. CONCENTRATION
Polymethylene polyphenyl.... 9016-87-9............. 80% to 100%
isocyanate
Containing 4,4 Methylene.... 101-68-8
bisphenylisocyanate (MDI)
(Approximately 40%-50% MDI)
Tetrafluoroethane (134a).....811-97-2.............. <15%

EMERGENCY OVERVIEW - Brown liquid. Slightly Musty. Sprayed or heated material harmful if inhaled. May cause allergic skin reaction. May cause allergic respiratory reaction and lung injury. Avoid temperatures above 105°F (41°C). Toxic flammable gases and heat are released under decomposition conditions. Toxic fumes may be released in fire situations. Reacts slowly with water, releasing carbon dioxide, which can cause pressure buildup and rupture of closed containers. Elevated temperatures accelerate this process.

INHALATION - At room temperature, vapors are minimal due to low vapor pressure. Excessive exposure may cause irritation of the eyes, upper respiratory tract, and pulmonary edema (fluid in lungs). May cause respiratory sensitization to susceptible individuals. MDI concentrations below the exposure guidelines may cause allergic respiratory reactions in individuals already sensitized. Symptoms may include coughing, difficult breathing and a feeling of tightness in the chest. Effects may be delayed. Decreased lung function has been associated with overexposure to isocyanates.

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How does something like this compare to the sheet insulation?

Metal boxes get hot in the sun.

If you had several small intake vents along the bottom and more at the top, you could use natural convection to draw in cool air and vent the hot air.

Inflatable beds are light, but they aren't warm in cold weather. The Murphy bed probably comes closest to ideal.

Sounds like fun!

Sue