Here's you answer: (Which I gave in my first post, but in my ignorance I had not read your question to shape it into an answer)
Temperature IS related to heat, here's why:
Take a sea and put in it a thermometer. The temperature reading will be close to atmospheric temperature. Right?
Now you take a cup of tea, and put in it a thermometer. The temperature will be higher.
Your argument is that the heat in sea is higher compared with the heat in tea. But this is not true. Let me explain.
When we measure heat, we don't measure the energy in the body, we measure the energy that moves. So, if you put the thermometer in sea, the energy that moves from water to mercury (Which then increases K.E. of mercury molecules causing them to rise) is heat. This is very small. If a large amount of heat had transferred in case of sea then we would have seen mercury rise even higher.
So in fact the heat is GREATER in case of tea than sea.
Another concrete reason is Newton's Law of Cooling which states that "Rate of heat transfer is directly proportional to the temperature difference", this means that the greater the DIFFERENCE of temperature between mercury and sea/tea, the MORE will be heat transferred.
You have confused the concept of Heat with Kinetic Energy and Potential Energy. Because the K.E. and P.E. of sea are indeed higher than those of tea.
Let me say it again, heat is the energy in move. Nothing possess heat.