Is heat released during work due to ATP breakdown or a increased blood flow?
Is heating of a body the result of increased blood flow or extra energy from ATP?

It is mainly because of the breakdown of ATP (Adenosine Triphosphate, a type of nucleic acid with an Adenosine base, a Ribose sugar, and 3 Phosphate groups), alternatively and more formally known as ATP Hydrolysis. During hydrolysis by water, ATP splits into Adenosine Diphosphate (ADP) and an inorganic Phosphate (Pi), releasing some energy. I'll explain more below how exactly this works.

How or why does ATP Hydrolysis release energy?

If you take a look at a diagram of an ATP molecule, you'll notice that it has 3 phosphate groups, each with a Hydroxyl group (-OH) that has a net negative charge due to Oxygen being highly electronegative and hogging electrons from the Hydrogen bonded to it. Consequently, you have 3 molecules with slightly negative charges attached to each other. If you've ever played with magnets, you'll know that like charges repel. So overall, the ATP is highly unstable because of these repulsive forces that are situated so close to each other. When the bond between the 2 inorganic phosphates is broken, a large amount of energy is released. Here's a diagram from Campbell's Biology 9th ed (note that the Hydrogens in the phosphates are not shown for simplicity):



When the last phosphate is broken off, you are left with one molecule of Adenosine Diphosphate (ADP) and an inorganic phosphate group (Pi). Energy has been released. However, this is not the entire story. Generally speaking, ATP Hydrolysis does not occur without another component: an endergonic process. An endergonic metabolic process is any which requires energy input in order to proceed. Think of it with the following analogy: imagine a ball trying to roll uphill by itself. At the bottom of the ramp, the ball is very stable and has low potential for performing work. But uphill, the ball would have a higher potential energy. It is impossible for the ball to roll uphill from a state of low energy to a state of high energy. Thus, we first need an input of energy--say the mechanical energy of our hand pushing the ball--in order for it to move up.

Our endergonic process (such as in protein synthesis by a ribosome or the phosphorylation of glucose in glycolysis, the first step of cellular respiration) requires some energy input from ATP in order to proceed in an exergonic manner--that is, in order to release energy without any help. With our analogy, this is like pushing the ball to the top of the ramp and then letting go, allowing the ball to roll back down from a state of very high potential energy (and therefore instability) to a state of low energy. The energy that we had to input from ATP is known as "activation energy", because it's literally energy that we need in order to unlock or "activate" an endergonic pathway.

Example of ATP Hydrolysis releasing heat:

When you have an infection in your body, your hypothalamus will raise the body's set temperature point to induce shivering. Shivering consists of many muscle contractions, all of which require hydrolysis of ATP. The result is a release of a large amount of heat that increases body temperature to a point at which pathogens cannot survive.

What about blood flow?

Blood flow does not actually produce heat by itself, but it can direct heat to the surface of the skin, such as when the body needs to cool down. The main source of heat in the body remains the ATP.

EDIT: much of the information here can be reviewed in this wonderful YouTube video by Andrew Douch