I’d like to give you an answer from a different perspective.
There are 2 things I want to shed light on: 1) Enthalpy 2) Enthalpy Change
- Enthalpy: the energy contained within a system under constant pressure
- Enthalpy Change: the energy (usually heat) given off or taken in by a system
When we measure the temperature of a reaction, we measure the enthalpy CHANGE, not the enthalpy. For reasons known to science, enthalpy can not be measured.
So, when you measure the temperature of a reaction & see an increase, it is an exothermic reaction because heat is being given out to the surrounding. So, we are actually measuring the temperature of the surrounding.
In an endothermic reaction, you will see reduction in temperature, i.e. the system is taking energy from the surroundings, so the surroundings lose heat & become colder.
As humans, it is only possible for us to measure the temperature of the surroundings, not the system.