We call it Thermology the part of physics that studies the phenomena related to heat, heating, cooling, changes in physical state, changes in temperature, etc. Thermometry It is the part of thermology focused on the study of temperature, thermometers and thermometric scales.
Temperature It is the quantity that characterizes the thermal state of a body or system.
Physically the concept given to hot and cold is a little different from what we usually use in our daily lives. We can define as hot a body that has its molecules shaking a lot, that is, with high kinetic energy. Similarly, a cold body is one that has low agitation of its molecules.
By increasing the temperature of a body or system it can be said that the state of agitation of its molecules is increasing.
As we remove a bottle of mineral water from the refrigerator or remove a cake from an oven, we realize that after a while, both tend to reach room temperature. That is, the water "heats up" and the cake "cools". When two bodies or systems reach the same temperature, we say that these bodies or systems are in thermal balance.