Exhaust fan and cooking time/temp

Cooking with gas releases harmful pollutants like carbon monoxide, nitrogen dioxide, and particulate matter, which can seriously impact indoor air quality and lung health. The priority should always be to remove those contaminants—not to worry about minor (if any) temperature changes. Ventilation is critical for keeping your home safe and healthy for everyone.

Multiple sources confirm this:
• Canada’s government emphasizes the importance of ventilation while cooking:
https://science.gc.ca/site/science/en/blogs/science-health/cooking-storm
• Washington’s Department of Health states that proper ventilation reduces exposure to harmful pollutants:
https://doh.wa.gov/community-and-environment/air-quality/indoor-air/ventilation-while-cooking
• Even when turned off, gas stoves can leak methane, making good ventilation even more necessary:
https://www.npr.org/2022/01/27/1075874473/gas-stoves-climate-change-leak-methane

If anything, your wife should be encouraging you to use the exhaust fan more, not less. The potential risk to your health (and your family’s) far outweighs any possible, barely noticeable effect on cooking temperature.

Great insight into how exhaust fans affect cooking time and temperature! This advice is invaluable for anyone looking to optimize their kitchen’s efficiency. https://hoodsly.com/

I don't think you are going to luck into any data on kitchen exhaust fans reducing cooking time. The closest I could come would be these sites-
https://www.acs.org/content/acs/en/pressroom/presspacs/2012/acs-presspac-may-30-2012/kitchen-exhaust-fans-vary-in-effectiveness-in-reducing-indoor-air-pollution.html#:~:text=The%20scientists%20found%20that%20none,speeds%20that%20hurt%20their%20efficiencies.

https://www.sciencedirect.com/science/article/pii/S0360132318301112
https://phys.org/news/2012-05-kitchen-exhaust-fans-vary-effectiveness.html

These studies just looked at how well the fans do the task of removing or reducing pollutants though- not if they change cooking temperatures. I would hazard to guess they don't, because the heat is being applied below the pad at a constant rate determined by your knob selection. In an electric stove, that's controlled by a thermostat, and the gas stove is just a constant valve control flame. It's not as if the fan is blowing cool air down on the pan, heck it's not even that good at pulling heat away. Especially not in summer, when the air outside is likely hotter than inside your home. If I needed to cool my kitchen, I would not rely on the hood vent fan to do the job. From past experience, when it's hot in the kitchen and outside, turning the stove on -even with the hood fan - is not a pleasant experience.