Yeah, an electrician is the best bet. The tricky thing is that they will have to reroute the wire through a different wall which requires going into the attic if your lucky or the crawlspace/basement which can be more difficult. Regardless, an electrician can probably cover it.

However, assuming you have electric heat, it is crazy to only have one thermostat for the whole house. You can save a lot of energy by individually regulating rooms with multiple thermostats. Either way, if you have an old spring type thermostats, consider replacing it with a digital timer model.

If you have central heating then your options are limited. Move it or you can try to insulate it. It may not be the most elegant solution, but I've had success in some situations with a styrofoam box cut to fit the thermostat.

I have another take on this.
If you examine your current thermostat, you'll find that it is basically just a spring dial with two wires running into the back of it.

Since the wires do not carry high voltage, they basically just carry the on/off circuit to the furnace. This means, when the temp in that room gets too cold, the contacts close and the furnace starts.

Conversely, if the room stays too warm, the contacts never close, and so, the furnace stays off. This is your problem.

While the idea of insulting around the thermostat with a styrofoam box is a way to make the thermostat less responsive, and will work, you could also consider relocating the device to another wall in another room.

Depending on the construction of the house, you could "fish a wall" (between the studs) to find the wires and pull them to a new location, OR, simply buy wire of the same guage, and like an extension cord, just extend the circuit to your new point on the wall and install the thermostat there.

YES, buy a new programmable, digital thermostat so that you can have the furnace run at different levels at different times or not come on at all when you're gone. It's worth the investment, but shop carefully so you know you have as flexible of programming that you need.

All that being said, it's NOT that hard to "fish a wall" nor is the screwing of a new unit into plaster board or wood all that hard. You want it about shoulder height, in an area not subject to drafts, nor next to a heat or cooling vent.

Also, in theory, you want circuit (low voltage or otherwise) to be a short as possible, to reduce loss due to resistance in the wire. So, plan your extension to be the shortest route possible (in front of the plasterboard if that doesn't bother you) or along the floor or ceiling if it does.

Ideally, you could use the existing wire to simply move to a different location... OR just run a new wire from the furnace to your new thermostat...and that's basically where the eletrician comes in.
You'll find they are familiar with the right gauge, have the tools, know what to do and not do, and work quickly to accomplish it in a fraction of the time that it might take you.

But if you're a do it yourselfer (DIY), you CAN do this yourself. They also sell books at Lowes, Home Depot, etc on basic wiring, though they concentrate on 110-120 voltage AC wiring like your wall outlets. And, if you're going to do THAT kind of work, well, yes, call an electrican and have him do it right the first time.

Good luck.