Barometric dampers are great, but they require considerable installation or duct work.
Your cooler shoud already be set up with a simple damper system. Just below the blower, outside the cooler (sometimes inside the cooler), there is a thin slot all the way across the duct(it might be covered with aluminum tape). Inside this slot, there are guides for a damper to slide into. You must slide a damper into this slot to block the heated air from going up into the cooler. This damper is commonly called a "cookiesheet damper". It is simply a flat piece of sheetmetal with a 1/2 inch right angle bend in it (used as a handle). The dimensions of the damper is the same as the inside of your duct. When you insert the damper, use some aluminum tape to seal over the "handle" of the damper and the opening (slot).
In the spring, when you are setting your cooler up for the summer, you must remove this damper and reseal the slot. At the furnace, there should be a similar damper that needs to be inserted in spring and removed in winter. This damper keeps the cooled air from escaping through the furnace.
If you don't have either of these dampers you can have them made easily and inexpensively at any sheetmetal shop.
To learn more service and repair information on evaporative coolers, visit:
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Larry Galpin The Cooler Doctor
Service, Repair & Enhance the Performance of Your Cooler Yourself and Save $100s Every Year!