Here’s an earlier thread that talks about how the value 1/3 is derived.

Here’s another thread that discusses the general purpose of EWA.

If those aren’t enough to give you the intuition that you are looking for, then I think the best idea is create a couple of sample sequences of temperatures and then compute the EWA with different values of \alpha and watch what happens. For example, create 50 samples where the first 10 or 20 bounce around with an average of 70 degrees (or 20 if you like Celsius ) and then start trending upward towards a mean that is say 10 degrees higher. Try it with \beta = 0.9 and then with \beta= 0.7 and watch the difference in behavior as you compute the EWA values for the whole sequence.

If that’s still not enough, then after doing the above I think you should just go back and watch the lecture again with all the above in mind.