Simply put... no, the nest is not the proper thermostat for your application. Most professional thermostats now have some sort of recovery feature that "learns" how your home heats and brings the temp up to the set temp at the programmed time. Nests claim to fame is that you don't have to program it for the time changes, but actually you are programming it and it takes a week or so to "learn" what times and temps that you make changes at the thermostat so you are programming it. There are other thermostats that do much more then the nest and allow you to control compressor and aux heat lockout temps. This is a better feature in that you can see more energy savings by controlling these options. Many thermostats now have access through internet protocol.
Again. The nest is not the correct thermostat for your application.