No it wont. Your nest thermostat will just cool or heat to the temperature you have it set it and will use that for all the rooms. What i do in my house since i am using 4 also. I have 2 rooms that always get to 71*F and the other 2 will be 75*F. So i sent my thermostat to the ones that are normally cooler and set the thermostat to 73 or 74. It will cool/ heat and stay in that range.