I find "think bright" is much more common usage, but why? In my opinion, "Think" is a verb, so it is reasonable to use adverb to describe it.
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Some shine bright, but never seem to hang around for long.
It was unnerving how bright they shone and so I tried to look away.
The sun is shining bright in the sky and nobody else is around.
According to OxforddIctionaries.com bright can be a noun, an adjective and an adverb, which has a literary meaning brightly (see the examples).