Make sure when using the IR thermometer that you have a good target for it.  I typically put a piece of black electrical tape on the surface.  Check both the header tank on the radiator where the hose connects and a spot next to the t-stat housing on the head.

If you have a working t-stat, the head should measure very close to the t-stat rating.  The header tank may be a couple of degrees lower.  If a 180 oF t-stat is really only letting the engine get to 170, try a new t-stat.  It sounds like the thermostat is stuck open.

Oh, I don't have an overheating problem, just the opposite.  I have the 180 degree Stant installed in the car now, but temp barely approaches 170.  I've had to resort to blocking off the grill to get it close to that temp during the winter but now the temp is usually in the low 40's, not exactly sub-polar.  I've cross-checked the temp on the head next to the spark plug using a laser thermometer and it is within a couple of degrees of the gauge indication. Coolant mixture is about 1/3 antifreeze, reading about 5 degrees on the tester.  

I would worry more about how you use your car, where you live, and your expectations than focusing on values printed in a manual decades ago.  I don't drive my Mini much in the cold and we have hot summers so I use cooler t-stats than the 190 oF one Alex recommended.  I have used both 160 oF t-stats sometimes but generally stay with 180 oF.  

Remember that fitting a t-stat won't fix an overheating problem, you are just using it to set a running temperature when everything else is working the way it should be.

54mm thermostats for GM products can be used in the Mini.  One example is the 180 oF Stant 29358 t-stat.

88° 'stat for unleaded fuel in a road car, unless you're in really high ambient temperature.

My factory manual states that a Cooper S should be equipped with a 170 degree thermostat but that was in the good old days of high octane leaded gas.  I've been told that considering the use of ethanol additive in pump gas these days, the best burn efficiency can be achieved using a higher rated thermostat, say 195F.  Thoughts?