Helen of Troy which owns Kaz, which owns Honeywell (one of the largest businesses specific to Nest's thermostat space) has a market cap of $1.7bil - http://finance.yahoo.com/echarts?s=HELE - that's why this sounds crazy.
On the flip side, P&G is a $217bil business - so, not that crazy how big the market is and can be.
EDIT: As larrys points out, Honeywell is a $70bil biz.
Definitely brings more sense to the 3.2b price tag.
On top of that, think of what those guys still have under the hood. Google wants to be the everything of your life. Smartphones fill a part of that but smart devices are another big chunk; and Nest was the company that is undoubtely leading a revolution on the field.
This isn't a strategic move to eventually dominate the thermostat market. This is a strategic move to eventually dominate the 'everything you need' market.
On the flip side, P&G is a $217bil business - so, not that crazy how big the market is and can be.
EDIT: As larrys points out, Honeywell is a $70bil biz.