I work around the corner and buy from Slow Beer often and have been buying from them since they opened. They're basically my local. I have never had a beer from them that has been past date or gone off, and I've drunk plenty from them. As far as I can tell they do not refrigerate their beers, except for a small amount for consumption in store. I'm not sure where they store their beers as they have a companion bar/store called Six Row and may have offsite storage as their shop is pretty small. However, they have very high turnover so beers don't seem to stay on the shelves more than a few weeks. Stock changes constantly. The store does not get hot in summer months. About half the store is antipodean, the rest is import. They seem to me to be focusing on locals and interesting imports.
I do, however, check any specialty large formats closely, as they keep them on a high shelf and it just doesn't seem like the best place to keep any beer, much less slow-moving large formats. The only beer I have ever bought from them that was close to the BB date was a month before it. It was from the top shelf and was an IPA. Really, I shouldn't even have bought an IPA that was 11 months on. It seemed to be in good condition, but the hops had mostly dropped off.
I myself wouldn't hesitate to buy from them by mail. Hope that helps.
