Nocioception (pain perception) in subcutaneous tissue
&quot;no nociceptors in subcutaneous fat&quot;

Well nerves innervate tissue, but only the layers of skin above the hypodermis (Subcuteaneous fat layer).
You are correct.
If one was to burn below this layer they would not feel pain in that area due to having no nociceptors.
There is a great Kharn Academy video on this topic here.