Think positive is an elliptical expression meaning think positive thoughts.
A section from Garner's Modern American Usage on this topic (bold added):
Adjectives vs. Adverbs. English contains a number of linking verbs (or copulas) apart from to be —e.g., appear, feel, seem, become, look, smell, taste. These verbs connect a descriptive word with the subject; hence the descriptive word following the linking verb describes the subject and not the verb. We say He turned professional, not He turned professionally. Writers frequently fall into error when they use linking verbs. One must analyze the sentence rather than memorize a list of common linking verbs, much as this may help. Often unexpected candidates serve as linking verbs—e.g.:
• "The rule sweeps too broadly [read broad] ." (The writer intends not to describe a manner of sweeping, but to say that the rule is broad.)
• "Before the vote, the senator stood uncertainly [read uncertain] for several days." (The word describes not the manner of standing, but the man himself.)
A similar issue arises with an object complement, in which the sequence is [subject + verb + object + complement]—e.g.:
• "Chop the onions finely [read fine] ." (The sentence does not describe the manner of chopping, but the things chopped. The onions are to become fine [= reduced to small particles].)
• "Slice the meat thinly [read thin]." (As above.)
An elliptical form of this construction appears in the dentists' much-beloved expression, Open wide (= open your mouth wide).