The thermostat needs to be controlling the surface temps over the heating mat. Where the probe goes can vary from set-up to set-up...but making sure that particular surface doesn't get too hot is its primary job.

You can get a digital thermometer that measures two different temps at once as well as humidity. (Acu-rite brand from WalMart or hardware store) Place one probe at the warm end (I like mine under the hide since that's where the snake will spend most of its time) and place the unit itself in the corner of the cool end. The probe gives you the "outdoor" temp and the unit will measure the "indoor temp" and humidity where it is sitting.

Will the UTH be enough to raise ambient temps? That depends entirely on the room the cage is in. However, in MOST American homes that are kept cool for our comfort....no, it won't be enough. Especially for a glass tank. You may need an additional heat lamp on the cool end to keep things warm enough overall...which can cause havoc with your humidity levels, but can be dealt with.

You should probably get it all set up well before putting any animal in it, and let it run for awhile, tweaking as needed until you dial in those steady temps and humidity.