Learn Farsi: امیدواریم چای سرد نشود. - We hope the tea does not get cold.

It is the negative present subjunctive of شدن (to become). It is made by combining the negative prefix نـ (na-), the present stem شو (shav), and the third-person singular ending ـَد (-ad) because the subject 'tea' is an 'it'.

I learned that subjunctive verbs start with بـ (be-). Why is it missing from نشود?

When you make a subjunctive verb negative, the negative prefix نـ (na-) completely replaces the بـ (be-) prefix. You never use both prefixes at the same time!

Why are we using the subjunctive mood for 'does not get cold' anyway?

In Farsi, verbs that express doubt, wishing, or hoping force the following verb into the subjunctive mood. Because the sentence starts with امیدواریم (we hope), the second verb must take the subjunctive form.

Why do we use the verb شدن (to become) here instead of a word for 'get' or 'be'?

In English, we say something 'gets' cold to show a change of state. In Farsi, we express this change by using the adjective سرد (cold) combined with the verb شدن (to become), meaning 'to become cold'.

Should there be a word for 'that' after امیدواریم (we hope)?

You can include the word که (that) and say , but just like in English, it is very common and completely natural to drop it.