gzt:

 

Handle9: How much heat do you think an extract rangehood actually removes from the space? It’s not a lot at all.

 

Lots and lots. An externally vented rangehood removes tons of heat. Essential in summer.

 

My rangehood externally vents in normal circumstances. There was a problem. I noticed the house was getting stupidly hot with the rangehood on. Later I noticed air was blowing out of it near the ceiling. On removing the cover I found no retainer was fitted to the motor/hose during installation and the vent hose was now detached from the motor. The unit was blowing all the heat out at ceiling level. Fixed the hose retainer. House temperature problem solved.

 

As a bonus in summer we run the rangehood when the oven is in use. It is surprisingly effective at keeping internal temperatures down by removing a proportion of the hot air generated by the oven and venting that externally.

 

While your anecdote is nice it really doesn't prove all that much.

The amount of heat removed by a range hood is really limited - it's essentially waste convective heat. Most of the heat from the cooker is transmitted into the cookware. From there it's radiated heat which a rangehood does nothing to solve.

A rangehood removes waste air which has some energy but not significant amounts of heat in the context of other heat sources. It's not nothing but it's far from significant compared to the other elements. 

I've worked in HVAC control for the best part of 20 years and never seen a rangehood used as a temperature control device because that is not what it's purpose is. It's used for the control of fumes and humidity.