If you're contemplating a deck fireplace, take a close look at the area you have to work with before beginning the design process. Unless your home is a mansion of Hilton-esque proportions, be realistic about your deck space and dimensions and how much room there is to work with. The fireplace you choose should be large enough to heat the space adequately, but small enough that it doesn't completely overwhelm.
Keep the fireplace from sticking out like a sore thumb by taking pains to incorporate the design into the surrounding space. Be sure to take foliage and existing décor into consideration. It doesn't have to look exactly the same as the existing house, but shouldn't clash with it, either, so choose a style that complements your home. Placement of the fireplace is a key issue, since it will affect the overall look of the deck. Where it ends up might be influenced by zoning codes, however, because they often require a fireplace to be a certain distance from the house. It's also important to think about how the fireplace will impact your view and aid your desire for privacy.