Bert feels cold.
This has been a relatively mild winter, but I think yesterday was the coldest day we've had this winter, with a high around 0°F, not taking the wind chill into account. That was probably one of the warmest coldest days we've ever had in January, but nevertheless, Bert's initial situation is certainly a familiar one to us South Dakotans (not that we have a monopoly on cold winter weather, of course).
I wish Ernie had been at my sister's house to help me out over Christmas. I was there for about three days, and the whole time I had on multiple layers and I was still cold. I don't know how my nephews and my niece manage not to freeze and turn into little kidsicles.
You know, I never noticed it until just this moment, but Ernie's misguided determination to keep Bert at a comfortable temperature is actually really similar to the way that Grover attempts to please his "favorite" customer, the blue and round-headed Mr. Johnson. I wonder if that's why you don't see Ernie and Grover together very often in sketches, i.e. they're too similar to create a good conflict.