Dyson makes quite a few internet-connected fans and air purifier s that already integrate nicely with Alexa. The ability to create a schedule based on air quality readings, for example, might be cool.
Was that pun intended? 
An easy way might be to use the Alexa Voice Service:
Hehe, actually, we use this fan more as a heater than a cooler so it actually didnât occur to me (so, no pun intended).
Iâve used voice control of the fan regularly with Alexa. In fact, my wife doesnât know how to use the remote, and only uses her voice. I was thinking about a scenario where the fan (and heat) comes on by itself depending on a number of different criteria (temp below a preset, which is of course is what a thermostat is for), but also taking into account if the sun out, are we asleep in bed or better still, getting ready for bed and would like the room to be a bit warmer - if it needs it.