The easiest approach is to use commercially available wireless environment sensors in each room, and have one Arduino receive the messages and summarize the results.
Many of the sensors (e.g. from LaCrosse, AcuRite, Oregon Scientific, etc.) are cheap, very reliable, have been hacked and are readable with a cheap 315 or 433 MHz receiver and Arduino board. Google a bit for lots of ideas.
Here is a big open source project that reads many of them. Here is how to hack others.
Also discussed many times on this forum, here, for example.