Both bars receive the identical left-end heat pulse at the identical instant. The advancing warm front follows the one-dimensional diffusion solution, so each front position grows as the square root of (diffusivity × time) — the race is decided by α alone. The conductivity slider changes how strongly heat floods in (color depth near the source), but it can never change who wins.
Normalized 1-D teaching solution (erfc profile, constant properties, ideal step at the left face). Real contrasts can be far larger than the slider range — the air-versus-water pair differs in α by roughly 150× while air conducts about 20× worse. Color depth is a relative-effusivity cue, not a calibrated temperature scale.