I would not cover the plants.  After I graduated I tried growing the same
CP outside on the covered patio of my apartment.  Almost all died.  I
think the open rooftop allowed radiant cooling at night, but a cover over
the plants prevented this (Barry could explain the thermodynamics involved).
>From my experience, the limiting factors for growing CP outdoors in the
AZ desert are not daytime heat nor excessive sunlight, but night temperatures
and water demands.
Michael Chamberland