There are many map projections. All of them are wrong, some of them are usefull (reminds me of statistical models...). Selecting a map projection that everyone is happy with is about as easy as peace in the middle east. What map projection you choose seems to be based on many factors, including how much calculus you know. (For a somewhat snarky discussion of map choices, see xkcd.) I am a mathmatician, and I like analytic solutions, even to my partial differential equations (as a result, flowing water mystifies me). This leaves about four projections. The Mercator projection is great for seamen navigating by sextant, but just as clearly only for that purpose. The Equalrectangular is computationally nice, but stretches the poles quite a lot. Unfolding the world into a isocahedron seems a bit extreme, even if it does look exceptionally cool. Sinusodial projections are ridiclous, they look pointy. The Robinson projection is not the most clever of projections, being defined by a table of pretty arbitrary values, but it works very well. It has the straightforward math of interpolation, and looks like a map of a round thing. There is distorion at the poles, but less than in the equalrectangular, essentially a compromise. Mapping the surface of the earth the same way the complex sphere is mapped to the complex plane clearly out of the question, which is the only projection with a clear mathematical advantage. So Robinson it is. (The selection of a map projection for smaller segments of the earth's surface is an entirely different problem, one best left to the USGS.)

I made the first version of the temple map several years ago, when
Pres. Monson mentioned that about 80% of LDS church membership lived
within 200 miles of a temple. I wondered how much of the globe that
was. With a little poking around I found lat/long coordinates for all
the temples, a simple map of the world, and started plotting. Green is
within 200 miles, gray is more than 1000 miles. A few times a year,
about as often as a temple is dedicated, I update the images. The
algorithm is not particularly elegant or efficient, but for something
that runs as infrequently as it does, it does just fine. Over the years
I have improved it, changed the colors, switched to the Robinson
projection, increased the resolution and detail of the maps. Although
its hardly a tool for precision navigation, it is now of enough detail
to give a pretty good indication of what areas are close to temples,
and which are not.

The calculation is not perfect, as it uses distance "as the crow flies" ignoring mountians, rivers, and roads. Actuall distance is thus a little farther than the map indicates. I like the distance 200 miles, both because it was the distance mentioned by Pres. Monson, and because it is probably the outer limit of a single day trip to the temple. 200 miles on good roads in a car is probably about 4 hours, give or take. This means a temple trip would include 4 hours travel there, 2-3 hours at the temple, and 4 hours back, with perhaps an additional hour consumed in eating, rest breaks, fueling etc. That's a 11-12 hour day. Long and tireing, but do-able. Much past that and breaking the trip into two days becomes the only feasable solution. This is also a break in attendance patterns at this distance. A one day trip, even if long, can be done monthly, or nearly so, assuming the cost of fuel is within reach. Two days severly limits the number of trips that can be taken in a year: arrangement for time off from work is usually necessary, child care gets exponentially more difficult, the cost of lodging becomes an issue. A working (ie not retired) family could feel fortunate to get to the temple twice a year, and once or less would be very common. A better indication for distance is thus time (4 hours one way) and if the cost of transportation is within reach of a typical family. Mapping this metric of course, would be much more difficult, as it would take into account varying economics, national borders, changing infastructure, an a host of other factors.