There are two reasons why we might expect to find ð rather than θ in this word.
First, the apparent cognates in other languages have a voiced consonant. The French word is bordel bɔʀdɛl, the Italian is bordello borˈdɛllo, the German is Bordell bɔrˈdɛl.
Second, the spelling th in this position (following a stressed vowel in a disyllable) regularly corresponds to the pronunciation ð: father, mother, brother, other, bother, feather, gather, whether, rather, slither, smithy, swarthy, worthy, Swithin. True, there are no other words in -thel except the names Bethel and Ethel, which both have θ. Even so, the pattern is very clear. Words spelt with medial th and pronounced θ are otherwise just those of Latin or Greek origin: author, cathode, lethal, method. But brothel looks and feels Germanic.
The OED reveals the reason for the exceptionality of brothel. It’s really not a cognate of bordel at all. The etymology goes back to Old English.
ME. broþel, f. OE. broðen ruined, degenerate, pa. pple. of bréoðan to go to ruinbut
The modern sense arises from confusion with an entirely different word BORDEL (q.v.); the brothel was originally a person, the bordel a place. But the combinations bordel-house and brothel's house ran together in the form brothel-house, which being shortened to brothel, the personal sense of this word became obs., and it remains only as the substitute of the original bordel.