We're looking for a way to turn on the air conditioning at our camp, say on a Thursday night, so that it will be cool when we arrive on Friday evening, but to shut it off if we don't go to the camp that weekend. Can you set a programmable thermostat to turn the unit on for a certain period of time and then automatically turn it off?
If the camp has internet access, you may want to look into a WIFI-controlled thermostat. Most allow you to remotely monitor and control the temperature through a mobile phone app or with a laptop web interface. This will allow you to have the most versatile control over your temperature settings. The only other piece of equipment you'll need to make this work is a compatible wireless router - you won't need to install an entire home automation system.
Otherwise, you need a true 7-day programmable thermostat. Check the specifications on the package, because each one will have different capabilities. The one I have allows for four different temperature settings per day, for all 7 days of the week individually. You may not need something with that high of a resolution, and can get by with a single set temperature for each day of the week. The general rule will be the less features a thermostat has, the lower the price.
There are also thermostat models labeled as 5-1-1 and 5-2, which allow separate temperature settings for Saturdays and Sundays. Note that a 5-2 will only allow a single setting for the weekends. As Chris mentions, you could fudge the week day settings and get by with one of these.
Depending on your location, it would likely be more economical to open the house up and circulate air with fans to bring down the trapped heat and then turn on the AC. It won't be cool when you arrive, but it will become tolerable very quickly.
If air conditioning is required, and you have some sort of network connectivity, I'd look into home automation. Call your cottage before you leave, turn on the AC, and have it cool when you arrive.
If your only option is a programmable thermostat, then you can use one, but it's the least desirable option. However, not all thermostats will give you the option of doing it on a Thursday. Many recognize M-F, S, S as the programmable days.
So set the date on the thermostat so that the thermo Saturday = real Thursday. Set the temperature, say 75 degrees F/ 24 deg C, to come on. Do the same for Sunday (Friday) Set all other zones to as high as it goes.
When you arrive on Friday night, manually set the temperature to the desired level for the rest of your trip, returning to programmed levels when you leave.