Hotspot temperature and equilibrium temperature difference?

In any chemical reaction, at the initial stage of catalyst use, the catalyst has high activity and the reaction releases a large amount of heat, causing the temperature to rise as the conversion rate increases; in the later stages of the reaction, the situation is reversed. The highest temperature that can be reached is known as the peak temperature. This is a theoretical concept. In actual production, the hotspot temperature is the temperature at the highest point of the bed. The equilibrium temperature difference should be the difference between the temperature at which the reaction reaches equilibrium and the temperature before the reaction started!

Understanding the hot spot temperature in production in that way is too one-sided, just my personal opinion; feel free to criticize it. If a catalyst bed has 6 layers (6 temperature measurement points), I believe the hotspot temperature should be the temperature of the layer with the greatest temperature difference within the bed, as the catalyst in layers above it has poor activity and cannot function effectively ； However, this layer cannot fully reflect the situation either; the subsequent layers will also experience temperature increases, so using the highest temperature point in the bed layer is not appropriate. The hotspot temperature can serve as an indicator of catalyst performance; as mentioned earlier, when there is no temperature rise in that layer (or only a very slight one), it can generally be assumed that the catalyst has become deactivated.