I’m not sure if this is where to post this, but here it is.
I came across these wood cabinets installed 24 inches over an island range top. There isn’t a range hood or any type of heat shield installed under the cabinets. I think there may have been a range hood installed there, but it could have been removed during a remodel. What is the rule of thumb for distance between the range top and bottom of a wood cabinet, or is this ever permitted?
Shold be around 30 depends on the manufacture of the cook top. See page 4. http://products.geappliances.com/ApplProducts/images/t07/0000008/r08209v-1.pdf
Typical mounting heights of cabinets would dictate that the sink base is at 36" and 18" between the upper cabinets and the upper cabinets are 30" in height for a total of 7’. When an exhaust fan is installed, the cabinet above it would be 18" therefore, with no exhaust hood, the cabinet would be 30" above the range top.
I see no problem with this other than the fact that you are not exhausting the steam or food odor out of the house and the humidity levels might increase.
Marcel:) 
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