Whether we record a temperature on earth or estimate the temperature of the big bang, we are dealing with the same class of rules and laws, of physics, and performing the same basic task of coming to a conclusion about the some hidden property based on some other observable properties.

The machines we make to measure temperature come from the same stuff as the universe does, so there isn't anything special with regard to reading a value from a machine vs. calculating a temperature based on the properties of the stars and galaxies in the universe. Therefore, regardless of when the temperature has occurred, or where it happened, we are still measuring it. And as long as it was written down, it has been recorded.