Heat will have EXACTLY the effect that you saw in this HR drift test. When your core temp gets out of its normal comfort zone the capillaries in the skin dilate and much more of your blood volume get shuttled to the skin to dump heat. That leaves less for the working muscles. The heart responds by increase it rate of contraction to try to keep up the demands for O2 in the muscles. The result is increased HR and perception of effort.
Getting your HR hung up in Z3 is usually a sign of aerobic deficiency.