There are two concepts here, temperature and heat. The temperature of a 'system' is only that property that determines whether or not a system is in thermal equilibrium with another system.
This accords with our experience that we can distinguish by touching between something that is hot and that which is cold but have little feeling if it is at the same temperature as we are.
We can measure temperature by many different means, such as pressure of a gas, electrical resistance, expansion of a liquid, magnetic susceptibility of a paramagnetic salt and by radiant emission, which is how we can determine the temperature of a furnace or of the surface of a star. The reference of zero is then some property such as the triple point of water for the celsius scale.
A molecular interpretation of temperature indicates that in a molecule with an infinite number of energy levels, as the temperature is raised more and more energy levels become populated but any given level always has less population than the one immediately below it. This is in accord with the Boltzmann distribution. Thermodynamically this is expressed as the rate of change of internal energy with entropy, i.e the slope of a graph of internal energy vs entropy (at constant volume).
( In systems where there are a finite number of energy levels, such as an arrangement of spins, (for example in some types of nmr experiments) then negative temperatures are possible, i.e. larger population in upper than lower levels. This does not mean a temperature below absolute zero.)
Heat is internal energy in transit, it flows from one part of a system to another, or between two systems both by virtue of a temperature difference, and can only be quantified when the transfer has finished. It is incorrect to refer to 'the heat in a body' just as it is incorrect to refer to 'the work in a body'. The heat and work are ways in which the internal energy of a body is changed. Put another way, it is impossible to divide the internal energy into some amount of heat and another amount of work. We have no direct knowledge of heat from our senses (or instruments) and heat is quite distinct to 'hotness'.
The first law defines the change in internal energy $\Delta U$ as the sum of heat $Q$ and work $W$, $\Delta U = Q+W$.
This means that we can define heat as that energy transfer brought about by non-mechanical means, and is equal to the internal energy change less the work done when the system is at a different temperature to it surroundings.
The first law has three features, (a) it is based on conservation of energy, (b) to satisfy (a) it introduces the idea of internal energy and (c) it defines heat as energy in transit by virtue of the temperature difference.
That heat is energy was first determined quantitatively by J. Joule in the mid 1800's in elegant experiments where the increase in temperature of water agitated by a paddle wheel, rotated by the lowering of a weight under gravity, was measured.
