so when a hot object warms a cooler object, temperature does not flow between them.

but are the temperature changes of the two objects equal?

No, the temp changes would be equal only if they had the same mass and were of the same material.

When a hot object warms a cooler object, temperature does not flow between them. Instead, heat flows from the hotter object to the cooler object until they reach thermal equilibrium, where their temperatures become equal. However, this doesn't mean that the temperature changes of the two objects are equal.

The rate at which heat flows depends on factors like the thermal conductivity of the materials, the surface area of contact, and the temperature difference between the objects. The hotter object will lose heat and cool down while the cooler object will gain heat and warm up.

The specific temperature changes of the two objects will depend on their initial temperatures, their heat capacities (a measure of the amount of heat energy required to raise the temperature of an object), and the amount of heat transferred. If the objects have different heat capacities, their temperature changes will also be different.

To calculate the temperature changes of the two objects precisely, you would need to know their specific heat capacities and the amount of heat transferred between them. Heat transfer equations, such as Fourier's Law of Heat Conduction, can be utilized to determine the rate of heat flow and subsequently calculate the temperature changes.