What type of remote thermostat are you talking about ?
I would like to install the Honeywell with WiFi like I have in my home. But I have to find someone that knows a lot more about it then I do, because I need it to operate 3 AC's or at least 2 of them.
I can share what little I know about thermostats.
A WiFi thermostat requires 24 vac unless you can find one that used batteries. If your furnace control board has a 'C' terminal then that will provide the needed extra 24 vac. If there is no 'C' terminal then you would have to add a 24 vac transformer. This would require 120 vac to operate.
You might also look at the connections on your current thermostat and look for a blue wire. This is normally the C wire.
I don't know what features all of the WiFi thermostats have, but if there is a Y2 terminal this should control a second AC. Y will control the first AC.
The Honeywell RTH9580 has a Y2 terminal.
If you have to add a transformer you will need a 6 conductor cable to the thermostat unless you delete the fan only function.
And of course like the description says you will need to have WiFi in order to control it from your mobile device.
That's all I got.
Peace
Dave