I do not know the official specs, but I have one near Phoenix for about a year now including last summer. I mounted it in a water tight electrical gray PVC box on which I drilled a hole on one side to run the wiring conduit. I think it was a 4x4x2" container. It is mounted behind a post so it does not get direct sun exposure, but does get the 100+ degree ambient. I use it with a Vegitronix moisture, humidity and temperature measurements. The powerline ethernet and wallwart are also outside under a deck awning.
I have a single zone drip irrigation system there and this would be a good application for using a relay output of the WebControl. My problem is that the existing controller is not in a good location to do something like this so I probably will not ever take that step. With last years data I can see that there was not too much variation throughout the summer so a timed controller is good enough and then set it bak in the Fall.
I do not think their manual has the temperature specs so giving them a call is a good idea. Your 60 degree is outside the commercial electronics range which normally has a 55 degree max. It has no heat sink on the regulator, so you will want to use someting like 7 volts at the connector if you do not want to generate excessive heat to get the voltage down to 5 volts. Adding a little fan would likely also help.
You could also be a little more creative and cut out some of the air conditioner cold line insulation and mount the electronics on top of it. It will stay nice and cold. It is a shame to hog all that cold when there are better uses than just keeping people cool.
http://www.amazon.com/Webcontrol-Universal-Temperature-Humidity-Controller/dp/B001H4JXLU
They sell two versions. The BRE is what I developed software. While both versions have support for internal logic, but new one has a better logic engine. Both have the same remote access and control capability via wired IP.