The diagram to which you referred may be common in the UK, but except in exceptional circumstances would not be legal under the building codes in most US municipalities, or in most of Canada, at least for residential use. (I haven't looked lately, but at my last casual browsing of Canadian codes, they appear to be much like the common US ones.) Any connection that carries line voltage must be enclosed in a "junction box." Any access to any metal part that carries line voltage must require the removal of one or more "permanent fasteners" such as metal screws or bolts. This pretty much precludes using a surface mount device, like the thermostats described, at line voltage.
Line voltage thermostats are used in the US, but usually only for electric baseboard/underfloor systems and some heat pump systems. Where line voltage is used, the thermostat itself usually is embedded into the wall in an electrical junction box. Even for these systems, current rules in most areas would require that the "thermostat" in your diagram be replaced by a "relay" or in some cases a "contactor" which would in turn be switched on/off by a low-volt thermostat hung in the occupied areas of the residence.
By implementing these restrictions in building codes, it is apparently hoped, by some of our leaders, that eventually the US will have even more "surviving idiots" than the rest of the world. It seems to be working...
You also asked about the use of bimetal thermostat sensors. The "sensing" in the simple mercury switch thermostats used here is usually done by a bimetal strip, usually a coil that looks like a clock spring, with a glass tube containing a slug of mercury hung at the outer end of the coil. As the temp falls the coil winds tighter and tilts the tube so that the mercury runs to one end and connects two embedded wire ends. A cute feature is that when the mercury runs to the turnon end it applies an additional torque to the coil, so that the temperature has to rise a bit past the original switch point before the blob runs back. Automatic snap-action.
The two adjustment pointers mentioned by Kendall (01 Oct 05 - 09:04 AM) are called "anticipator" adjustments and are usually on a couple of small rheostats that apply a bit of extra heat near the bimetal coil. One heats the coil a little when the mercury switch is OFF (for the heat circuit) - making the switch turn on at a little lower room temp, and the other heats it a different bit when the switch is ON, also making it turn off at a different slightly lower than room temp. This lets you adjust the "gap" in temperature between when the furnace turns on and when it turns off, although it may shift the calibration between switch point temp and indicated room temp if used too agressively. Digital thermostats generally have similar adjustments, although they often work by applying a voltage bias to a thermister circuit.
The "OFF Side" anticipator adjustment would normally be critical only if you're using the thermostat for heating and cooling. (Older 2-wire 'stats often only had a single anticipator.) In a heat-only setup, setting the Off-side one too high could get an "off below on" condition, but it's really unlikely. It does sound as if dianovan may have managed it. If one or both of these is set too far off, you'll often see fairly wide temperature excursions. If the heat comes on at 68F (20C?) and stays on until the room hits 75F (24C?) you're likely to feel like you're enjoying the benefits of menopause. Some twiddling may be in order. A swing of about 2F (1C) is generally considered acceptable, although some sensitive souls have trouble even with that.
Simple flat leaf bimetals with "dry contacts" may be more common in line-voltage setups, but it's really difficult to get sensitive temperature adjustment with sufficient "snap" to prevent arcing of the contacts. They're commonly used here for water heaters and such, where adjustment in 10 or 20 degree F increments is sufficient, but seldom seen - so far as I'm aware - in room temp setups.
I've been told that A/C is uncommon in the UK, but it's one of the easiest ways to get rid of that muggy humidity, and in moderate temperatures shouldn't be too expensive to run. I'd suspect it will become more common when more Brits have been exposed to it here... I've even seen A/C equipped houses in Seattle - proof positive that it's becoming more common in foreign places.