In Greek. Or am I mistaken about its having originally been /tʰ/? I thought the difference between τ and θ was the former was /t/ and the latter was /tʰ/.
That’s correct, and jheem is right that there’s evidence for early fricative pronunciation, but only in a very limited region. Geoffrey Horrocks in Greek: A History of the Language and Its Speakers (pp. 112-13) says:
Neither Teodorsson (1977) nor Gignac (1976) finds any compelling evidence for the corresponding shift of the voiceless aspirates /ph, th, kh/ to fricatives /f, θ, x/ in Egypt in the Hellenistic, Roman imperial or early Byzantine periods… There is, however, direct evidence that /th/ > /θ/ in Laconian [i.e., the Doric Greek spoken around Sparta—LH] in the fifth century BC… Thus, though the evidence is frankly meagre, it would perhaps be reasonable to assume that fricativization in the Koine began in various areas outside Egypt during the Hellenistic period and that it had been widely, though by no means universally, carried through by the end of the fourth century AD.