And: it's not really so easy to define "active warzone". As said, hundreds if not thousands of commercial planes fly over conflict zones every day, successfully.
Just to pick a random example: Flight TK7900 IST-SIN is up in the air right now (19:32 GMT on Oct 13, 2015). For a picture of the route, see this.
http://tinyurl.com/obzlxxv
Over the past few hours, it crossed from Turkmenistan/Iran to Afghanistan a bit north of Herat, crossed the country, passed south of Kabul, then went on to the Pakistani tribal area south of Peshawar, and continued across the hostile Pakistani-Indian border just south of contested Jammu and Kashmir, and then continued over India. There's plenty of conflict in these areas.
Then it was on the Indian Ocean, far away from anyone who could rescue it should something happen to it. Right now it is passing Andaman Islands. If it were forced to land due to multiple engine failure, the passengers perhaps would meet the Sentinelese people.
https://en.wikipedia.org/wiki/Sentinelese_people
And I think Turkish Airlines is perfectly OK to do all this. Should someone shoot down the plane, I know some people would blame the airline. But I would only blame those who shoot it down. It's not okay to shoot down airplanes. Commercial airplanes are not valid targets.