Supposing that the subject of the noun clause is, in fact, presently, and intrinsically, the best, would the correct sentence be:
I heard [that] you are the best man for the job.
or
I heard [that] you were the best man for the job.
or perhaps either?
The argument for the former is that "is" more accurately represents the time window during which the subject is the best, whereas the argument for the latter is that tense agreement between "heard" and "was" is aesthetically pleasing.
Perhaps also supporting the latter is that "was" does not contradict "is"—per Hedberg, 1990s: "I used to do drugs. I still do, but I used to, too."