Not a correct assumption.
When we feel the effect of heat energy, energy is still intangible. No matter how much we want to, it will never become tangible as you seem to suggest so it's impossible to say something like "heat energy itself".
If we do feel the effect of heat energy, well, then we feel the effect of heat energy.
I think that, itself, would be a reasonable analysis. This, rather, is due to the fact is because energy is intangible. You cannot pick up 5J of energy here and there.
If there is something extra that I don't understand, can you please clarify? Thanks.