This smartapp uses any temperature input to control the High, Medium, Low speeds of a ceiling fan based on your desired room temperature setpoint turning on each speed automatically in 1 degree differential increments (adjustable). For example, if you set your desired room temperature setpoint at 72, the low speed comes on first at 73, the medium speed comes on at 74, the high speed comes on at 75. And vice versa on decreasing temperature until at 72 the ceiling fan turns off.
A notable feature is when low speed is requested high speed is turned on briefly to overcome the startup load then low speed is engaged. This mimics the pull chain switches that most manufacturers use by always starting in high speed.
There is a motion option so that the fan turns off automatic mode when no motion is detected. A thermostat mode option allows the ceiling fan to be controlled automatically by the smartapp or manually using the device handler. Currently this smartapp works specifically with GE 12730 Z-Wave Smart Fan Control or Leviton VRF01-1LX designed specifically for motor control. I use the custom device handler by @ChadCK Z-Wave Smart Fan Control Custom Device Handler
There is an update for a compatible 4-Speed zigbee version of this smartapp for the new [Hampton Bay ZigBee Combo Fan/Light Controller] (Home Decorators Ceiling Fan/Light Controller MR101Z - First Impressions) using this new custom device handler. Click on this link if you are interested in downloading the working beta version of the 4 Speed Ceiling Fan Thermostat - Zigbee.
Shout out to @whoismoses Eric for his contribution making it Parent-Child based smartapp. It will be the start of Version 2.
I modified the existing Virtual Thermostat which can only do on-off to make it work specifically for 3 Speed Ceiling Fan control.
This is the actual Ceiling Fan installation from the discussion on Control 3-speed Ceiling Fan and Light Kit. I use to do this fan control with Rule Machine and although it works adequately it was cumbersome to make a simple room temperature setpoint change due to the number of rules that needed to be modified. Now that Rule Machine is no longer supported I needed to get something to replace it and wanted to make it more user friendly. Edit (CoRE using pistons replaces Rule Machine)
How To Install 3-Speed Ceiling Fan Control smartapp
If you need help installing this custom smartapp @JDRoberts gave some excellent step-by-step instructions here