How can we talk about a single temperature if the early universe was in local thermal equilibrium? If the early universe was only in local thermal equilibrium, how can we talk about a single temperature for the whole universe?
 A: Ah, I studied this question earlier this semester as well for a cosmology course I took in my university. It's a part of inflationary universe model.
The early universe was only in local thermal equilibrium, yes. The observable universe, that is.
I'm going to digress a bit to explain the inflation model: Imagine a balloon being blown until it is so big that an ant standing on the balloon thought that the balloon is flat. A similar thing happened to our universe (in this model). The early universe underwent an inflation; it expanded so large that the spacetime curvature looks flat to us now, in the present day. This, by the way, is the "flatness problem" found in modern cosmology.
Now, as for why we talk about a "single temperature for the universe"; imagine the balloon again. Perhaps some part of the balloon is at a temperature of 7 degrees Celcius, and let's say that some other section of the rubber of the balloon is at 10 degree Celcius. To an ant standing within the first region, they will all say that the balloon is 7 degree hot, while ants that live on the latter section of the balloon will say that the balloon is 10 degrees.
Similarly, in our observable universe, we observe a "Cosmic Microwave Background Radiation" (the famous CMBR). This radiation permeates the universe, and in our section of the universe (i.e. our observable universe), we observe a more or less uniform temperature of that radiation (I recall the CMBR in our observable universe is around 2 Kelvin).
TL;DR: Because the universe inflated, hence we have a (locally) uniform temperature for the observable universe.
Hope it helps!
