BLUE TONGUE SKINKS

Next week is my 18th birthday and I've already been told I'm getting $248 plus a surprise bonus so I'm sure it will be enough to get everything I will need for my BTS. I have just one question for now but I'm sure I will have a lot more once I bring my little buddy home.

The enclosure I am getting is a 36"Lx20"Dx13"H. It is a custom enclosure that is designed to hold heat well. The only problem is that it has a built in incandescent light fixture. Can my skink get injured by the light because of the height of the enclosure or will my skink be fine since they're bodies are low to the ground? I think the skink will have 8-10 inches of space between the light and the floor of the enclosure.The enclosure I am getting does not come in any taller sizes.

I agree with Edward, it totally depends.
See if you can get enough heat on the basking side without using the built in light. If you must use it, then you must also make sure to not put anything underneath that light that could raise your skink up, nothing he can climb on.
For example, if this is the basking side, put a simple flat floortile under the lamp, straight on the floor of the tank, not even any substrate under the tile, and then make sure there is nothing on the sides that he can climb up on.
Eight inches to the lamp isn't quite high enough that a determined BTS won't be able to reach it.
To be ABSOLUTELY sure he won't get injured, don't use the built-in fixture. If you MUST, then try to use the very minimal wattage bulb.

My adult IJ, standing on the tip of his tail and scaling the walls of his tank, comes just a couple inches away from reaching the lid. The tank is 18". I'd be a little concerned about the height of your tank, especially when you figure that any basking bulb is going to be at least 3-4" long.

Consider maybe using a very low-watt bulb or even just a UVB bulb that doesn't get hot, just to provide light in the tank, and some other type of heating device to provide the heat. My preferences would run with a RHP (Radient Heat Panel) inside the tank (bit expensive but safe, last forever, provide top-down heat) or Heat Cable/Tape/Pad underneath on the outside.

If you go with the heat tape/pad, be sure to get a thermometer that will protect the skink from it getting too hot and burning. With an RHP/heat cable you don't really have to worry as much IMO.

Also, you may want to consider upgrading to a larger size when you can. I have one of mine in a 75 gallon aquarium (I believe it is 48 x 18 ). That gives ample room to walk around in and divide the cool and warm side of the tank. The other is a 55 breeder tank, which has the same floor dimension but is only 12 inches high. The skink in that tank was a rescue and is not able to get up on the side of the tank, so I don't have to worry about him climbing up or getting out. I would never try and keep my other one in a tank that shallow. Unless your enclosure is fully enclosed on the top, you can expect that your skink will be able to get out. And even if it is enclosed, they are sneaky and determined animals and will try to find a way if it can reach the top.

oh yes, i've had 2 escapes, luckily i found them both...never underestimate the will power of a bluey! They WILL find a way to get out if you arent careful XD