If you can redesign one of your cupboards as a microwave barn somewhere other than above the stove i d do it.
Do over the stove microwaves have exhaust fans.
However exhaust fans are recommended for removing odors heat smoke and fumes that collect above the stovetop.
Recirculating fans and duct vents are both popular options for people who are interested in clearing exhaust food odors hot air and humidity from the kitchen when using over the range microwaves.
Virtually all building codes require a ventilation system installed over the kitchen stove.
It gives needed light and has a 3 speed exhaust fan.
This ventilation system has a light that illuminates the stovetop surface and a fan that removes smoke and steam from the air.
Over the range microwaves have a light and fan built into the bottom of the appliance.
And it s out of the way when not in use and only 1 1 2 inches deep.
Since a range hood protrudes further it also does a better job of capturing smoke steam and cooking odors and venting them outdoors.
While both varieties claim to clear the air of odor and heat one system is far superior to the other.
However they also have built in exhaust fans which serve as a stove top ventilation system to.
I have a great jenn air exhaust fan and light that retracts under the cupboard over my stove top.
Over the range microwaves can vent to the outside or can recirculate the air.
Range hood over stove for venting.