sending room temp data from multiple esp8266's to Mega 2560 to control CH gas boiler
I am also in the middle of converting the control of my heating, multi-zone, but using Ciseco / Wirelessthings units as temperature sensors both inside and out. See https://www.wirelessthings.net 

Simple serial interface is all you need from the Arduino to run these on a network. The coin cell battery lasts for over 1 year running 1 sample / 10min - the sample rate is configured but obviously the more samples you send the more the battery drains. Range seems to be OK and gets through 3 floors in the house and from the outside. I do use external antenna on the Arduino wireless unit to ensure I get all of the sensor readings.

However sounds like your house is BIG if running 3x WIFI extensions where as a single WIFI base station does me fine.