As we have discussed before, penetrating (drying) oil finishes tend to heat up while it is curing. However, once the finish is cured on the wood, there is less risk of spontaneous combustion. It will be beneficial to ensure that the wood is fully cured before using it.
In terms of any external heat, check with the manufacturer and see the label on the bottles. It is vital to understand if heat can break down the finish in case it is exposed to high temperatures. This is especially important in the case of any wooden utensils.