If they use some specific waveform that is identified on the other side then it should be either perfectly accurate or fail to measure anything depending on background noice - not lose precision. Reflections from the walls is what I'd be more worried about.

The biggest source of error is actually the variation in the speed of sound. It increases around 2% when the temperature increases 10°C. Then there is a source of error because it seems the clock frequency of the ADC/DAC on the iPhone is not 100% accurate. If you recalibrate the app with a known distance (by moving the temp. slider until the displayed distance matches the actual distance) it should be pretty precise. No warranties, however. If the noise level is too high, it usually just doesn't show the measurement. There's one other source of error, that was actually the hardest to filter out: The sound doesn't only travel on the shortest path (line-of-sight) but on many paths. And often the sound from the longer paths arrive amplified, compared to the shortest path.

It's too bad that the temperature sensor in the iPhone isn't accessible through the public API.

It has the hardware to measure temperature, but we can't use it.

(See: http://www.iclarified.com/images/news/3832/14751/14751.png )

Random guess: this may not be a full temperature sensor but just an on/off switch that is triggered when the temperature is above some limit.

It would require an Internet connection, but GPS + some weather API would do.

Weather APIs know the indoor temperature?