Anise.

Not sure what you mean by a small Christmas tree in shape. Do you mean you want a conifer? Something to prone into a triangle (conifer or not)?

Also, you don't mention SIZE at all. But I am thinking shade, heat tolerance and conifer (and ignoring the size issue). How about a Japanese Plum Yew. Only, not sure how they would like the particular part of Texas in which you reside. They are quite popular in the Southeast and other humid areas (up to maybe Zone 7), easily available at local garden centers. There is a vertical and horizontal growing variety. The one in the picture is the more vertical grower. I have both (in sun and deep shade). The ones in the sun seem much more slow growing compared to the one in deep shade..., which is kinda rare for a conifer. P.S., Despite the name they are NOT yews (they are in the genus Cephalotaxus). I only got into them because I had to rip out my Yews which are not deer resistant, the Plum Yew is highly deer resistant as another positive attribute. P.S., There is also Osmanthus heterophyllus 'goshiki' (which you can prune into whatever shape you want. Good luck!

http://www.onlineplantguide.com/Plant-Details/501/