The three words that should be capitalized in the sentence are "winter", "talk" and "town". Thus, the sentence should look like the following:
- "Winter was becoming famous, especially when she appeared on television in the show Talk of the Town."
We can see that, in the context of the sentence, "Winter" is a proper noun, a woman's name. Therefore it should be capitalized.
In any case, the first word of a sentence must be capitalized, even if it is a common noun.
The reason why we must capitalize the words "talk" and "town" is because they are the main words in the name of the show.
There is no need, however, to capitalize "of" and "the". They are a preposition and an article, respectively, which means they are not the main words in the name.
With that in mind, the sentence should look like this: "Winter was becoming famous, especially when she appeared on television in the show Talk of the Town."
