Question

Could the thermal energy of a bowl of hot water equal that of a cold water? Explain.

Answer 1

Sure, that's possible.  If the cold bowl has more water in it than the hot bowl does,
then the total thermal energy in the cold water could be as much or more than in
the hot water.

Think about this example: 
A man is sitting outside, next to a swimming pool in which the water has been
heated to about 70 degrees.  He's holding a steaming hot cup of coffee. Which
do you think has more thermal energy in it ... the pool at 70 degrees, or the hot
cup of coffee ?

Answer 2

No. Assuming that the two bowls are of same size and the containers are made of the material and the quantity of water in both the bowls is same, the one with hot water would be having a higher thermal energy than that containing cold water.