I have a 27 x 36 foot shop with 10 foot ceilings, 6" of insulation in walls and about 12" in ceiling, location is southern WI.  My floor is 6" of cement with pex tubing, heat supplied by LP fired water heater. During the week thermostat is at 60 and on the weekends when I spend the most time out there it is at 68. When the thermostat is turned up it takes several hours to raise the the temp 8 degrees.  I was out there for 10 hours today (68 degrees)and the pump never started once, 28 degrees outside. 

Is it more efficient to leave the heat turned up or drop it during the week?

OK, I'll bite Every BTU you put into that building will ultimately escape. The greater the temp difference, the faster the heat transfers, of course any wind will speed the process. IF you are not using it full time, I think it is more efficient to set it at a temp that will meet the unoccupied needs. IE: nothing inside will freeze and the equipment and surfaces inside will stay above the dew point. If you use it at regular times, a timed/programmable thermostat could prep the space for your comfort, hours before the expected use time. It would then go back to the unoccupied temps.

Say for example: You set it at 50F during the week(might be able to go that low or lower, depends on your humidity levels). Lets say you typically get out there by 9AM on Saturday. You set the system to start heating the space about 1AM on Saturday morning so it is up to 68F by 9AM(just an example, have no idea how long your slab takes to get from 50-68F) Say you normally stay out there till 3 or 4 PM. Since the slab will remain warm for quite a while, the thermostat could go back to the midweek/low set point probably around noon, so it is just starting to feel cooler about the time you are out the door anyway. For unanticipated use some sort of faster acting space heat to get to a comfort level quickly might be a good idea.

Hi ronmar, Thanks for your input. The setback of the temp is what I am presently doing. When the temp is raised it takes a long time of heating water to bring that slab back up. I do sometimes run a small electric heater to speed up the reheat but then I see a rise in my electric bill.

Cement floors are not a good way to heat an area unless you want it to be at a constant temp all the time. They just take to long to heat up. Then you are pouring all kinds of energy into heating them up to only be in there for a small amount of time. All that energy is just wasted.

You know that the thermal lag time is about 8 hours, so it should be pretty easy to use smart or programmable thermostat to start the recovery ramp with sufficient lead time to be warm (or close to warm) while you're there.

In many/most markets a cold climate mini-split heat pump will be dramatically cheaper to heat with than propane. Using a floor thermostat set to keep the slab at 68-70F while you're there and a mini-split to control the room temperature may be worthwhile if you're going to keep the place for more than a few years. Taking a WAG at the heat load you'll probably do just fine with a 1-ton mini-split a 1.25 tonner at most) and turning the slab heat OFF during the week. Both the Fujistu 12RLS3H and Mitsubishi -FH12NA have modes that will keep it at 50F when not in use. A 1-ton would be able to deliver ~14,000 BTU/hr or better when it's 0F outside, 60F inside, which is probably about half the burner output of the propane water heater running a 100% duty cycle (which it clearly never needs to do.)

https://portal.fujitsugeneral.com/files/catalog/files/12RLS3H6.pdf

https://portal.fujitsugeneral.com/files/catalog/files/15RLS3H6.pdf

http://meus1.mylinkdrive.com/files/MSZ-FH12NA~MUZ-FH12NA_Submittal.pdf

http://meus1.mylinkdrive.com/files/MSZ-FH15NA_MUZ-FH15NA_Submittal.pdf

When it's 20F outside and the mini-split is modulating in it's mid-range with a 68F interior temp it'll be delivering 3x the amount of heat per kwh that a resistance heater would. (And you also get high efficiency air conditioning out of the deal.) When it's 20F outside and 50F inside it'll be about 4x.

With the propane fired system as backup you also have some flexibility.

Running flat-out to ramp up the room temp a 1 ton mini-split won't have the same efficiency as when modulating, but it'll be half the cost of getting that heat with an electric space heater. Flat-out it would be deliver heat at about the same rate as 4,000 watts of space heater. Most standalone plug-in space heaters top out in the 1500-2000 watt range, so the recovery time should be half or less.

With 15 cent electricity (the WI average is about 14.5 cents) at a COP of 3x you're looking at more than 10,000 BTU/kwh, fewer than 100kwh per million BTUs (MMBTU), so you'd be at less than $15/MMBTU with a mini-split, assuming an average outdoor temp of 20F.

A gallon of propane burned at 82% in a hot water heater delivers 0.82 x 91,600 BTU/gallon= ~75,000 BTU/gallon into the building, so it takes 1,000,000 /75,000 = 13.3 gallons per MMBTU. With $1.50/gallon propane (WI average propane price is $1.60 this week) that costs about $20/ MMBTU.

If you know how much propane you burn heating that space per year you can estimate the marginal savings, and factor that into the decision.