The 6L6 does take less heater current but it's a lower power valve too. I suspect to use it, ideally you would need to rebias the output stage and probably consider lowering the screen voltage. In any case the Quad output stage is somewhat unique, so any other effects might be too!
You can find data sheets for both valves (and many others) here:
http://www.tubedata.org/
39C doesn't sound particularly hot for electronics- bear in mind that many Quad II amps would have been hidden away in cabinets when new- operating it out in the open probably reduces the temperature usefully. Possibly a quiet fan would do more to reduce temperatures than drastic action like changing valves.
Chris