Changing thermostat in apartment?

I want to change the thermostat in my apartment (landlord said its okay) with one that has Bluetooth to connect to my iPhone. Or at least one with a controller. The one I have is super basic. My main idea is to wirelessly change the temperature or at least have it turn on based off of time. Not just how cold / hot it is. Such as at 11:30 when I go to sleep I want it to turn on for 30 minutes then turn off.

Any who. Mine is called a Robertshaw 9500. I don't know anything about these so can I just go to the store or online and buy any thermostat? Or is there a specific type. Like lets says only ones that are compatible with Type A.

I have a wireless thermostat - it's a Danfoss? Basically I can have six time slots during the day so I just program what temperature I want my house to be during my six chosen time slots. If the house falls below the temperature it's supposed to be at, the heating automatically comes on. I would just make sure that whatever you get, you get it properly installed by a qualified person. That way, you know it's done properly and if it isn't, you can demand repair.

Look online for the thermostats and see which is compatible with the one you now have AND be sure to do 2 things (1) get written approval from the landlord that it's OK to make the change and (2) keep the old thermo so that when you move, you can reuse it and take the wireless with you

You can get a progarmmable thermostat at any hardware or building supply store for $30 or $40. They are not Bluetooth controlled but just have a digital controller that you can program to come on and off several times a day that you choose in advance. The program can be tailored for different settings every day of the week. They also have a manual override so you can turn up or down until the next programmed change kicks in. To have one that is Bluetooth would be hundreds of dollars to get a master home control system. For what you want, and for a rental unit, the programmable type will be more than adequate.