obviously all the core jet e flux is sent out the back when using thrust revers, which again is perfect for causing catastrophic fires (Concorde)
The core jet efflux comes out of the back of a high-bypass turbofan engine whether or not the thrust reversers are being used.
Hot-stream reversers, which featured on early RB211s, JT9Ds, etc, were one of those things that everybody thought was a good idea at the time, but then realised weren't actually doing very much to slow the aircraft down and were therefore removed.
Incidentally I'd be fascinated to know what you think thrust reversers had to do with the Concorde accident.