Fire protection gear can be bought in Goron City. You can buy or brew fireproof potions that will temporarily protect you from the heat. To brew them, combine fireproof lizards or smother wing butterflies with a monster part. A woman also sells them by Foothill stable.

additionally you can also find a hylian guy who has side quest on the way to goron city, in a goron mine, that rewards you with one of the fireproof gear peices.

just go to the horse stable on the road to goron city and talk to a lady there

theres an NPC that sells elxairs at Foothill Stable

for desert you can use cold protection at night