While I agree that .22cal centerfire cartridges will kill deer, I would not recommend same for deer. Regardless of the shot in the heart/lung area, deer can go to far, in many cases, with holes through and through. One thing cannot be denied; bigger bullet equals bigger wound channel. Bigger wound channel translates into more rapid hemorraging. The more the animal bleeds the faster he goes down.
Add to that the case of trophy deer presenting a bad angle for your well placed shot, using a 22. This could be walking straight away from your position or at a steep raking angle. In those cases, you need a bullet that will penetrate a lot of deer meat and maybe bone, before reaching the certain, quick kill area. We all owe it to the game to make every attempt at getting quick, clean kills.
I began hunting deer with a rifle chambered for .243Win. I saw for myself that deer could be hit through the heart and still go 100 yards or more. One ran, jumped a stock fence, as if he'd never been hit and disappeared in an overgrown field, 20 minutes before dark. Just by luck, I found where he'd laid down in heavy cover. When I dressed the deer, his heart was cut into a "Y" by my bullet. After that, I began using a .270Win, which anchors deer with the very same shots that I had previously seen them run off on.