Also translates as "they are not swift". Is threre something subtle making the translation "they are not hot"? Or is it just general context, and in this situation both translations would be correct?
The adjective "iute" can mean either swift (= fast, quick) or hot (= spicy, piquant).
Both meanings are valid in that sentence above, but my first guess was that it refers to some edibles that aren't spicy.
You have to pay attention to the form of the verb and of the adjective:
Eu nu sunt iute - I am not hot/swift Tu nu ești iute - You are not hot/swift El/Ea nu e/este iute - He/She/It is not hot/swift Noi nu suntem iuți - We are not hot/swift Voi nu sunteți iuți - You all are not hot/swift Ei/Ele nu sunt iuți - They are not hot/swift