Can our bodies control which temperature we feel?

If you take a cold hand and press it against the warm part of your body thinking that you're using it to cool off that warm part, you feel the cold, and if you do it thinking that you're warming up that cold hand. . .how is it that we can control that? Try it, you can only feel one temperature at a time.Can our bodies control which temperature we feel?
Look at this question from a physics standpoint. When we feel cold, we feel heat being absorbed, or an endothermic reaction from a chemistry standpoint. When we feel warmth, we feel heat (or energy because heat is a form of energy) being given off or an exothermic reaction. When you put a cold hand on a warm part of your body and you feel cold, it is because you're hand is absorbing more heat/energy than the warm part of your body is giving off. If you feel warmth, your body is giving off more heat/energy than your hand is absorbing. So in reality we can't control which temp we feel. It all depends on the temp difference between your hand and that warm part of your body