Interesting discussion... I'm not sure there is a "right" answer, as there are a lot of variables. It might help to try and break down some of the issues...
First off - task analysis:
You have a washer full of X pounds of clothes, which are soaked with Y pounds of water that is left over from the spin cycle. The drying job is to evaporate those Y pounds of water. This is going to take so many BTU's of energy per lb, doesn't matter whether we are talking about cordwood, greasy coveralls, or the wife's unmentionables... (note however that the X:Y ratio may change depending on the type of clothes) It also doesn't matter whether those BTU's come from solar / wind drying (aka clothesline) a rack in the basement, or a clothes dryer. Call this the "key task" as you MUST accomplish it, or plan to sleep on the sofa due to low WAF. :red:
However all methods consume additional power in the form of delivering the BTU's needed for the key task - this is things like blowers, fans, dryer tumblers, the energy to drag that basket of clothes out to the line, etc. Call this the secondary power consumption. In the "perfect world" one would like to just use the amount of power needed for the key task, and keep the amount of secondary power to a minimum, but other issues such as time, type of secondary energy needed, WAF of the finished product, etc. is going to cause us to use secondary power to some degree. As a working assumption, I think it's safe to assume that saving time, or increasing convenience will increase secondary power consumption. Increasing WAF is likely to increase it as well, but this depends on the W (i.e. a preference for the feel of line dried stuff would lower it...)
The power for both the key task and secondary power can come in many different forms, some more suitable for different drying techniques than others. In sticking with the question of a tumble dry clothes dryer, the secondary power would consist of the blower, the timer, and the drum turning motor, all of which are almost certainly going to be powered by electricity. The power for the key task can come in any number of forms, most commonly gas (LP or Natural) or electricity.
The question is whether we can replace the key task power with hydronics, and if doing so is worth the time and effort. The secondary power is going to stay electric regardless, unless you want to hook up a belt to the wifes exercise bike (Caution, this approach is likely to have a LOW WAF!! :lol: )
There are two or three parameters that would go into balancing out the choice of what we use for key power - availability, convenience, and cost of the different forms among other things. There is also a desire to minimize the length of time it takes to do a drying cycle, as longer cycles are hard on the clothes, and the secondary power consumption is a function of time. There is also the limitation that one can't apply excessive heat due to the risk of damaging the materials.
Now for some numbers...
1. I've read somewheres that the over temp cutout switch on most dryers is supposed to open around 180*F, which is consistent with Willman's comment that his manuals say desired operating temperature is 135-165*F
2. I know that the amount of electric power drawn by a gas burner is negligible, thus measuring the electrical consumption on a gas dryer should give a very close number for the secondary power requirement. We have an older Whirlpool natural gas dryer, probably about 14 years old, fairly basic model, I would say about as typical as one is likely to find. I just put a "Kill-a-watt" meter on it, and find I am drawing about 325 watts starting out with a large load of mixed clothes. As the clothes dry, the power draw goes down (makes sense as the load gets lighter it should take less juice to tumble it) when the clothes were nearly dry I was showing about 275 watts. This is a significant difference, but not a huge one, I think it is safe to assume a constant 300 watt secondary power consumption to keep the math simpler.
About 3-5 watts is the timer switch motor. There was no noticeable change in the power draw between the Low, Medium and High heat settings. (which tends to confirm the negligible power draw for the burner assumption)
I forget for sure whether this dryer has a seperate motor for the fan, or if it just has one motor that both powers the fan and turns the drum, but I'm pretty sure it's the latter. Either way, I think it's reasonable to assume that secondary power consumption
3. The amount of moisture that can be removed by a given volume of air going through the dryer is going to be a function of the relative humidity of the air, which in turn is a function of the input air humidity, and how much / if the air is heated. It doesn't really matter HOW the air is heated. (Exception - Gas dryers will add some extra moisture to the air as water vapor is one of their combustion byproducts, but I'm not sure how big a factor this is, probably not much)
As a corrollary of this, the heaviest, drippiest item will still dry on the "Air fluff only / delicate" setting if you just let it crank long enough. Obviously this will reduce the amount of power consumed by the key task, but increase the secondary power consumption. One could draw a graph showing the relationship between power consumption on the secondary side, and power on the key task side as a function of dryer temperature. I don't know the exact curve shapes, but it is pretty obvious that as temperature goes up the secondary consumption would go down due to shorter drying times, and the key task consumption would go up due to energy spent heating the air. Assuming there isn't a time issue, the logical "best" drying solution would be to pick where the sum of the two power figures (and costs) intersect.
4. According to some of the other threads here about doing water / air heat exchangers in HVAC systems, it was sounding like you CAN get 120-150* air from such an exchanger, which would work in terms of Willman's desired operating temp statement. However secondary consumption might go up if you are at the low end of that scale.
Thus the key question IMHO is whether there are any savings in heat production costs (remember you have to power the boiler to make the BTU's, circulators, any extra blowers, etc.) and if that is enough to offset any increase in secondary power consumption.
Gooserider
If you could dry laundry with low air temps - appliance manufactures would only heat air to that threshold. 
