Two glasses of water have the same thermal energy so do they have to have the same temperature

Before answering this question first we have to understand temperature and thermal energy.

Thermal energy of a substance is defined as the sum total of kinetic, potential etc. energy of the substance. When two bodies come in contact with each other, the part of the thermal energy is transferred from hotter body to the cooler one which is called heat.

Temperature is the physical quantity which gives the direction of heat flow and determines whether two thermodynamic systems are in thermal equilibrium or not. Temperature of a thermodynamic system is a measure of average kinetic energy of that system.

If two systems have same average kinetic energy, then two systems must have same temperature. The temperature of a substance increases or decreases due to the change in average kinetic energy.

As per the question the two glasses have same thermal energy. It is told that the two glasses must have same temperature which is wrong. It is because thermal energy does not mean the average kinetic energy of the glass. Kinetic energy is a part of thermal energy.

Hence two glasses may be at different temperature depending on their average kinetic energy.