Currently there is no support for setting a thermostat’s temperature or mode via the emulated_hue component.
There is a workaround that folks have been using by create a script: Simple script to enable Amazon Echo / Alexa to set the temperature on a climate / thermostat device via the emulated hue component and Simple script to enable Amazon Echo / Alexa to set the temperature on a climate / thermostat device via the emulated hue component
It would be really awesome and simple for users if the emulated_hue component supported climate devices, more specifically thermostats. That way they can be exposed as a light entity to Alexa and the temperature can be set via brightness, in the same way that volume is set via brightness in the media_player component. For dual setpoint thermostats both setpoints would be exposed and controlled separately, as in, a heater and an AC device.