Learn Italian: Voglio una bevanda che non sia troppo fredda.

Because you are describing a drink you want to find, not a specific one you know already exists. When a phrase starting with che describes an undefined or desired thing, Italian uses the subjunctive mood to show that this is a requirement you are looking for.

If I changed una bevanda to la bevanda (the drink), would the verb change too?

Yes! If you said Voglio la bevanda... or Voglio questa bevanda..., you are talking about a specific, real drink that you know exists. In that case, you would use the regular indicative mood: Voglio la bevanda che non è troppo fredda.

Often we use an infinitive after verbs like volere. Why doesn't that happen here?

The rule about using an infinitive after verbs of wanting only applies when the subject is the same for both actions (like "I want to drink"). In this sentence, the subjects are different: you are doing the wanting (voglio), but the drink is the thing that might be cold (sia). Because the subjects are different, you must use che and a conjugated verb.

Does sia mean "I am" or "it is" in this sentence?