According to the 2006 International Building Code Table 720.1(2). , 3-5/8" of brick is just slightly under the Fire Resistance Rating for 2 hours of a wall fire. On the other hand, a 3-5/8" brick wall with a 1" air gap, does satisfy the 2 hour fire resistance code. The real question is, is 2 hours enough for a fireplace? A contained gel canister hardly constitutes a structure fire (burning at 800 degrees F as opposed to 1800 degrees F), but I guess anything can happen, right?
DISCLAIMER: Although all the following calculations are done conservatively, I can not guarantee these numbers are correct, so if anybody else can confirm, that would be appreciated.
Doing some math (and using this Nuclear Regulatory Commission calculator, spreadsheet 5.1), I've determined that a single canister of gel fuel, 6 inches away from a brick (facing the 1.5" x 8" side) will raise the average temperature of said brick roughly 10°F per hour.
The calculator says that a flame of ethanol 2 inches in diameter will have a radiant heat flux of ~90 BTU/(hr-ft^2). (As a note, it also calculates a ~6 inch flame height and 2525 BTU/hr heat output (which at 2.5 hrs is 6313 BTU), so this is probably a conservative calculation)
Also, if an average brick weighs 5.5 lbs, and the specific heat of brick is 0.22 BTU/lb-°F, then the thermal mass of a brick is 1.21 BTU/hr (5.5 lbs * 0.22 BTU/lb-°F = 1.21). If the face area is 0.1388 ft^2, we can calculate the average temperature change of the brick (90 * 0.1388 = 1.21 * T_delta/hr), where T_delta/hr comes out to be 10°F per hour.
Therefore the average change in brick temperature is 10°F per hr (assuming a single canister and the flame being 6" away). So if 3 ethanol canisters are burned simultaneously for 3 hours, the average temperature of the bricks will be 90°F warmer. For reference, UL testing reference temperature is 110°F over ambient. Also, hot water pipes are 120°F-140°F degrees, and those are often run along wood beams and drywall without any issue.
We can take this a step further by calculating the temperature gradient across the brick. A common brick has a thermal conductivity of 0.048 BTU/(in-hr-°F), so assuming steady state conditions (very, very conservative here), the brick should have a temperature gradient across it of 71.7°F [0.048 BTU/(in-hr-°F) * 3.63in / (90 BTU/(hr-ft^2) * .1388 ft^2) = 71.7°F]. If the average temperature of the brick has increased by 90°F, then the back face will only increase by ~54°F (90-(71.7/2)=54), which is well below that 110°F "safe zone".
I purchased a faux stone fireplace yesterday, which I believe is made out of some cement / stucco mixture, possibly with fiberglass in it as well. It was meant for gas, and has a warning on it to not exceed 22,000 BTU. The thickness of the entire body, including the hearth and back wall, were no more than 1"-1.25" inches thick. Since 3 gel fuel canisters only put out 9000 BTU in total, this should be more than sufficient.