Temperature matter when beer is clearing?

Hi All,
I've got a beer that's done fermenting (hit FG estimate, constant for 3 days), that is now in a clearing tank to get some of the gunk out of it. It was kept in the upper 60's (fermentation temp, not ambient) during the first 3 weeks. Now that the main fermentation is over, and it's just clearing and cleaning up the rest of the nastys, would taking it out of the water bath and having it at mid/low 70's ambient mess up any of the flavor, or do anything else that might be bad?
Thanks!

I don't typically secondary anything except my lagers.

The colder the beer the faster it will clear. I typically crash my ales down to the 30s if my fermentation chest freezer is free. If not it goes to a keg and goes to the storage box (60s) until there is room to chill it.

I personally would secondary the beer colder than 70 if possible. I don't think it will hurt anything to store it a week or so at ambient until you can keg/bottle.

Thanks, I need the space in my swamp cooler, so I'll just leave it (in the clearing tank) in there for another week and bottle.

On a side note, I probably would have just left it in the primary another week for clearing, but there was some pretty crazy frothing/krausen on the top of the carboy from earlier that, frankly, looked like poo and kept the beer pretty full of floaty pieces of nastiness. I figured moving it to a clean secondary for clearing would at least get it away from the krausen gunk on top, and also away from the huge layer of sediment on the bottom.

I wouldn't worry about the temp is at now. Although it will clear faster at cooler temps, it will also clean itself up at warmer temps as the yeast consume an diacetyl and possibly other unwanted byproducts that may be in there. It's not necessary, but it wouldn't hurt.