Can a 110v 3-wire thermostat be hooked up to a 110v 2-wire condo setup?
The King Model ESP120-R is not compatible with your wiring.  The third wire is the neutral, which this electronic thermostat requires to be operable.  Your original thermostat functions as a temperature controlled switch, connecting or disconnecting the heat without any need for externally supplied power.  Either you need a new replacement thermostat that also uses no separately supplied power, or you need to have your wiring altered.