The two blocks attained the same teemperature because energy was transferred from the warmer block to the cooler block.
The term thermal equilibrium refers to the fact that if two bodies that are at different temperatures are made to be kept together, heat energy is transferred from the hotter to the cooler body untill the both of them attain the same temperature.
Now, the reason why the two blocks attained the same teemperature is that, energy was transferred from the warmer block to the cooler block.
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