Why is it written like this, and can it be written in all hiragana instead?
If you mean the word “hot”, it’s written that way because it’s a foreign word and those are written in katakana. You can write it in hiragana but it wouldn’t be correct.
It’s written that way because と is the adverbial marker for onomatapoetic words. Similar to how に is the marker for regular adverbs. The と makes it clear that the meaning is the adverbial meaning (to feel relieved), rather than the full katakana meaning ホット (regular English meaning of ‘hot’). Note that many adverbs will appear this way, and exceptionally short ones will almost always have と as a standard part of the word.
Edit - to answer your original question, yes, it may all be written in hiragana instead. When part of the word is in katakana, it is usually either to make it obvious for the reader, or for emphasis.