If a cup of coffee is at 90°c and a person with a body temperature of 36°c touches it, how will heat flow between them?

According to II law of thermodynamics the heat always transfers from high temperature to low temperature body without aid of any external energy. So, according to this law the heat transfers from cup of coffee to the person body until both bodies reaches to the equilibrium state.

After attaining the equilibrium state, the heat transfer may be ceases between the bodies.

Whenever the person touches the hot coffee, he senses the heat that means the heat is transferring in to his body.