What brand is the wine fridge? Also, I'm considering replacing a wine rack (that butts up against a Jenn-aire downdraft stove ) with a wine fridge. What are the clearance issues, if any, that I should consider?

All the appliances are Jenn Air. Check the manufacturer's product information for clearances. There shouldn't be any issues locating the cooler by the stove; both appliances are insulated.