I totally agree with you about feeling worse in the heat, but that said, my HR is definitely higher when I work out in the heat for the same activity. Sometimes 10-20 beats more for the same pace. Which would be borne out in the TSS, does this not occur for you?
From other personal experience I think it could be the humidity that really makes it tough because I think running in very hot but dry temps is a lot more bearable because at least your sweat actually evaporates ?
As a person who is from a swamp but now lives in a desert, I feel the opposite. The dry heat dehydrates me so quickly.