Take a basic 12" table fan and set it on the kitchen floor, pointed toward the stove room. Run the fan on low speed. In about 30 minutes you should get a notable temperature increase in the kitchen.
For several years I put up 3M inside storm window shrink plastic. It's almost perfectly clear and worked very well. You apply it with their double-stick tape and then use a hair dryer to shrink the film tight.
I was able to test a fan yesterday, not a table fan like your suggestion but a tower fan. I put it on the floor pointing directly line of sight at the stove from about 10 feet into the kitchen. Unfortunately, after a hour, it made zero difference. I tried it at different spots in the kitchen and never got a temperature increase. I'll keep experimenting and report back if I get something to work.