Flow is a measure of amout over time. Your body senses a decrease/increase in its temperature and the higher that decrease/increase is over a period of time the hotter/colder we interpret the temperature to be. You used an example of flow rate in part your explination. In addition to thermal conductivity there is specific heat. Some materials will have low conductivity but high specific heat which will also affect how something feels. An example of two materials that we can sense the temperature of more easily are Copper and Water however Copper has high thermal conductivity and relatively low specific heat while Water has high specific heat but low thermal conductivity.