The diagram is for three materials with different thermal conductivities. I think number 1 is the material with higher thermal conductivity because it transfers the heat faster so it gets to the steady temperature sooner than the other two. Am I right? If not or if my reasoning isn't correct, I appreciate your help.
$\dot{Q} = k A \frac{\Delta T}{l}$
$l$ thickness
$A$ surface area
From this follows that besides other factors the rate of heatflow is proportional to the thermal conductivity $k$.
$\dot{Q} \propto k$
Therefore a high thermal conductivity allows for a fast heat transfer, hence your interpretation that a fast change in temperature correlates with a high thermal conductivity is right.
