if you cant touch the hot oil it is too hot and will COOK the leather
what we like is to wash the leather first with warm water containing a large squirt of dish detergent and a handful of baking soda
this will start to adjust the leather pH
let it dry out of the heat or sun on newspaper for a while but not to total dryness
then treat with Leather Honey (used to be Harness Honey)
just wipe it liberally on with rag and let it soak in
repeat til it wont take more of the top dressing
if it is strap goods - slowly and gently start to work the leather strap in a loop and straighten movement
if you see cracks in the leather it may be just too far gone
but it cant hurt to try
best of luck