The simulations on this page show how heat capacity affects temperature change and heat flux: 1) The volumetric heat capacity (VHC) affects the thermal diffusivity — the larger the volumetric heat capacity is, the slower heat conducts; 2) If the work piece is connected to other pieces, the volumetric heat capacity of those pieces can affect the heat conduction in the work piece as well.
Before you run the following two simulations, predict which thermometer and heat flux sensor will record higher values. You may be surprised.