OYou can use either who or whom; both are correct grammatically.
It's common to use "who" in place of the object pronoun "whom". The use of the whom is formal or less common in speech and writing.
Furthermore, the who/whom is a relative object pronoun in the relative defining clause "who/whom I thought was thoroughly honest". You can drop the who/whom. Besides, you can also use the structure think + someone + adjective. So you can also drop "was" in the clause. The sentence can be rephrased or reduced as follows:
The man (who/whom) I thought thoroughly honest proved to be a swindler.