I'm now voting against the sensor being an issue.
I see these as the most likely issues.
Mentioned at the beginning were a faulty thermostat. If it sticks open or partially open, then engine will never reach operating temperature............ that explains the gauge never moving much.
A clogged heater core was mentioned. That would explain cold air blowing from the heater.
Since the heat gauge on the dash doesn't move much, if at all, that makes me go back to the thermostat being failed in the open position.
Here is some information on that mechanical fan clutch.
http://en.wikipedia.org/wiki/Fan_clutch
Within this article it says:
"Another potential symptom of fan clutch failure (always drawing air at a high rate) in a cold weather climate is that the heating system blows lukewarm air never delivering sufficient hot air"
These thermal clutches do fail.
http://www.aa1car.com/library/cooling_fan_clutch.htm
This article mentions that the clutch should be replaced at the same time as the water pump:
"
Many experts say it is a good idea to replace the fan clutch at the same time as the water pump if the water pump has failed. The reason is because both age at about the same rate, so if the water pump has failed, the fan clutch may also fail soon. As as we mentioned earlier, a high mileage fan clutch may be slipping excessively increasing the risk of overheating.
When you buy a replacement fan clutch, make sure you get the same type (thermal or nonthermal) as the original. You can always upgrade from a nonthermal to a more efficient thermal fan clutch, but never the reverse. Or, you can get rid of the fan and clutch altogether and install an aftermarket electric fan kit to cool the radiator"
Here's what it says about diagnosing a fan clutch:
"CHECKING THE FAN CLUTCH
A good clutch should offer a certain amount of resistance when spun by hand (engine off, of course!). But if the fan spins with little resistance (more than 1 to 1-1/2 turns), the fan clutch is slipping too much and needs to be replaced.
If the fan binds, does not turn or offers a lot of resistance, it has seized and also needs to be replaced.
Fan speed can also be checked with an optical tachometer, by marking one of the fan blades with chalk and using a timing light to observe speed changes, and/or listening for changes in fan noise as engine speed changes.
You should also try to wiggle the fan blades by hand. If there is any wobble in the fan, there is a bad bearing in the fan clutch, or a worn bearing on the water pump shaft. A bad water pump bearing will usually cause the water pump to leak and/or make noise, but not always. Remove the fan clutch and see if the play is in the water pump shaft. If it feels tight (no play or wobble), replace the fan clutch."
So first, check to see if the fan blade is hard to turn when the engine is cold........... and hot......... engine off of course.
The fan clutch will allow the fan to be turned by hand. If it's overly difficult to turn, it may contribute to, or be the cause of the problem.
If it seems OK, replace the thermostat with a good one like Stant.
http://www.stant.com/index.php/english/products/consumer-products/thermostats/superstat-thermostat/
There is a thermostat brand called Fail Safe, but I think I would avoid that one. I've read good and bad things about it.