What is the best way to get rid of a draft originating from an air conditioner sleeve?

I have an air conditioner sleeve in my apartment and there is a gap towards the bottom of the front of the sleeve that is somewhat wide. I am not the least bit handy, and have a maintenance guy in this complex who isn't that fond of me, so I try to avoid having the guy in my apartment just to keep myself from getting aggravated. I had thought the gap had to be caulked, but knowing how far from mechanically inclined I am, I think I'd even something that simplistic up, so I was thinking of buying an air conditioner sleeve cover such as the one you can see in this link: http://www.conservationmart.com/p-279-indoor-air-conditioner-covers-window-sealing-endraft.aspx Do you think this would effectively work even if there is a bit of a gap where air is getting into the apartment, or would it have to be caulked to really end this relatively bad draft?
 
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