The transfer of heat between two objects touching is called?

When a cold object and a hot object are in direct contact (touching) heat will be transferred through thermal conduction.

Normally, heat transfer processes are categorized as thermal conduction, radiative transfer or convection.

Heat transfer through thermal conduction is the direct transfer of kinetic energy from one molecule to the nearby molecules. Because temperature is directly proportional to kinetic energy, interactions between neighboring particles exchange energy and that exchange energy gradually works it way from the higher temperature regions to the lower temperature regions. The process of the temperature becoming the same is called thermal equilibration.

Convective heat transfer occurs in fluids. If a gas, liquid, or other fluid, changes in fluid density change the buoyancy and will cause fluid to flow (a process called convection) and the heat contained in the warmer fluid is transferred to a new location by the physical movement of the fluid.

Radiative transfer occurs when a hot object radiates electromagnetic energy. While the sun is an obvious source of electromagnetic energy, it is also generated in smaller amounts by any object. The hotter objects radiate more electromagnetic energy and the cooler objects absorb it. This radiative transfer is important but not as noticeable usually as the other two. It does occur between objects whether they are in direct contact or not, but is usually so small as not to be important of the objects are touching.