Can you add thermal energy to an object without increasing its temperature? Explain

Yes. Thermal energy of an object is made up by the total kinetic and potential energy.

Kinetic energy depends on the temperature, the higher the temperature is, the more kinetic energy the atoms has. The atoms move faster and collide with each other.

Potential energy changes when change of state. When solid melts into liquid, potential energy increases. The atoms pulls apart from each other. Potential energy is the force between atoms in the substance. The more apart the atoms are, the higher the potential energy is.

So, 100°C of water and 100°C of steam even though has a same temperature, but has a different thermal energy. The potential energy is different. Therfore, we can increase the thermal energy of a substance without changing the temperature.