Learn Hardcore Turkish: Kestane sıcakken daha lezzetli oluyor. - Chestnuts are more delicious while they are hot.

… daha lezzetli olur: <a class="border-b border-dotted border-blue-400 dark:border-blue-500 cursor-pointer text-inherit no-underline" href="/grammar/turkish/verbs/aorist-ir">aorist (general truth, neutral, a bit more standard).
… daha lezzetli oluyor: <a class="border-b border-dotted border-blue-400 dark:border-blue-500 cursor-pointer text-inherit no-underline" href="/grammar/turkish/verbs/present-continuous-iyor">progressive used conversationally to state habitual tendencies or generalizations; very common in speech.
… daha lezzetlidir: with -dir , sounds formal/definitive or emphatic. The sentence with oluyor reads as a natural, experience-based generalization.

With adjectives/nouns: sıcak + (i)ken → sıcakken.
With verbs, you typically attach -ken to the aorist 3rd-singular form: gelir + ken → gelirken (while coming), okur + ken → okurken (while reading). You’ll also hear the progressive variant with -yorken in speech, e.g., geliyorken.

Why is it written as sıcakken with a double k?

Because it comes from sıcak + iken. In everyday Turkish, iken contracts to -ken, and when the word already ends in k, you get kk: sıcakken. The same happens in words like soğukken (from soğuk + iken) and yokken (from yok + iken).

Can I say sıcak iken, sıcak olduğunda, or sıcak olunca instead of sıcakken?

Yes, all are correct with slight nuances:

sıcak iken: more formal/literary.
sıcakken: the common, natural everyday form.
sıcak olduğunda: when it is hot (neutral, a bit heavier).
sıcak olunca: once/when it becomes hot, with a mild sense of a change/threshold.