Another example of an arbitrarily selected zero point is longitude. This was not always measured from the Greenwich meridian - Paris has been used, and the ancient Greeks (Ptolemy, specifically) used an island believed to exist off the west coast of Africa* in order to avoid dealing with negative numbers.
Really, though, none of the examples anyone have mentioned do what temperature does in terms of having a natural zero point which is not universally used. All of these examples (as of this posting) are either logarithmic scales (and all have a true zero point at negative infinity), are measuring position rather than quantity.
And you can't do this for time because of relativity - there's no reasonable point of reference for the International Terrestrial Reference Frame (i.e. the time kept by an ideal clock on Earth's surface at sea level) at the beginning of the universe, so we can't measure from the big bang even if we could otherwise determine the "age of the universe" down to the nanosecond.
Temperature has an arbitrary zero point because people have been measuring temperature since before the fact that there is an absolute zero was discovered.
*Of course there are such islands, but it's not known which he used and none correlate precisely to his maps.