storing beers at 70°

Why do you think it would be bad? Beer sits on store shelves all the time at that temp. Depends on the beer but you're not going to kill anything at 70 degrees. Light is the main thing to avoid here.

 

What beers/ kind of beers? It may influence the answer

 

I have generally the same question. My "cellar" is sitting around 68 degrees since it hit spring. All of my beers are stouts or barleywines, save for the few DFH 120s I have in there.

 

If you are going to age them for years, then there will be a difference. But anything under a year I can't imagine any larger abv beers having too much an issue. It just a little faster than optimal in above 55 degree temps.
Also a beer cellar makes it easier to regulate temp (imagine warmer climates and people at work 9-5 during the summer). Going to get higher than 68 indoors.

 

Yeah, as people are saying, they will age (or blend, lower in heat, balance) out a little faster than if they were at 55. So long as you aren't allowing them to fluctuate from like 50 degrees to 70 too quickly, and if you don't let most of them go for longer than 18 months, I think you should be totally fine. And...

Because to keep them at a consistent temperature (specifically 55) is most advantageous for a finely tuned age. Sometimes higher temperatures offset some of the characteristics that are subtle thus bringing others to the forefront that aren't as good. I'm trying to think of an example off the top of my head but am coming up short.