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it might pick up heat easily whenever it momentarily faces the sun, My understanding is that it must NEVER EVER face the sun, even for an instant. The sensitive instruments would be destroyed.
Its orbit around the L2 point combined with the annual revolution around the sun, allow it to examine all parts of the universe, except Earth, since in order to view Earth, it would be facing toward the sun.
It must never face the sun, or like this:
Or like myself after a night of drinking.
They put those elaborate multi-layered sun shields on for a purpose. It looks away from the sun, tilting only slightly in its year-long orbit to look at most of the universe during that time. It would be nice to have a 100 foot wide sun shield, but they had to cram all that crap into a tiny rocket.