OK. The fact that there are three wires may be, as you found, irrelevant. The only way to be sure what's going on is to go to the equipment and determine what the wires are hooked to there. In almost every system, red is hot and the other wires are different modes. For example, in 90% of the systems in my area, this is what you find:
red = 24v to stat
white = call for heat
green = call for fan
yellow (sometimes blue) = call for cooling.
There are others too such as:
orange = reversing valve for heat pump
blue = second stage cooling
various colors = second stage heating
In your system, it sound like simple continuity between red and white gives heat. Your circulator is controlled by a relay at the boiler, so the stat has nothing to do with it. Therefore, if that third lead isn't used, you can connect it to the common terminal on the secondary (24v) side of the transformer to allow your stat to run off the transformer. However, it also sounds like you said that stat won't do it. Therefore, after a very long-worded reply (
), my point is...
Exchange the stat and see if it gets better.
PS - Only mess with the wiring if you are comfortable doing so. Always kill the power to the transformer, usually by a switch or disconnect at the equipment, before messing with the control wires. If you have any doubts in your ability, call a professional. I don't want you to accidentally short a transformer, or worse, a control or ignition module, as those are $$$$$$.
Hope it works out!