How much Power ("energy") can a human body metabolize?

According to Stanford around 2000 watts in short bursts or 300-400 watts sustained.

This from studies interested in using metabolic energy to power implants, they wanted a baseline of how much energy was theoretically possible. Without knowing what time interval you want this is about the best you are going to get, how much energy the body can put out over minutes is drastically different than over seconds because they involve drastically different metabolic pathways and limiting factors.

A zeroth order approximation from first principles

Let's try to arrive at a Fermi approximation of the maximum sustained primary energy production of the human body.

("Sustained" is important. The human body can output 2 kW or more of mechanical power, corresponding of about 7 kW primary energy production, for a brief period of time, using ATP and oxygen already stored in the muscles. Sprint runners use this mode of operation.)

Disregarding all the details which make the joy of biochemistry, the human body produces energy by burning glucose. The gross reaction is

$$mathrm{C}_6mathrm{H}_{12}mathrm{O}_6 + 6mathrm{O}_2 rightarrow 6mathrm{CO_2} + 6mathrm{H_2O} + 2{,}880 text{kJ/mol}_{text{glucose}}$$

The human heart pumps no more than about 2 $times$ 100 mL of blood per beat, and the maximum heart rate is about 200 beats/minute, giving about 20 liters of blood per minute in the systemic circulation. One liter of fully oxygenated blood contains a little less than 0.3 grams of oxygen. All in all, you have no more than 6 grams of oxygen per minute to burn your glucose.

6 grams of oxygen is about 0.2 moles. Since you need 6 moles of oxygen to burn one mole of glucose, you cannot burn more than 0.03125 moles of glucose per minute; times 2,880 kJ/mol, we get a top theoretical energy prodution rate of

$$90 text{kJ/minute} = 21.5 text{kcal/minute}$$

That's about 1.5 kW, for those who care.

I can make a very rough calculation assuming that the maximum heat loss for a body in water corresponds to a power of about 24 kW, and "immersing a person in iced water" is not enough to lower his temperature in case of severe TFMPH poisoning.

Therefore, the human body can produce at least 24 kW of heat.

TFMPH, as well as other proton translocators, causes exactly what you describe: "causing every cell in the body to spontaneously metabolize as quickly as possible" (it is used for this purpose in some highly illegal "weight loss" concoctions).

However, be advised that this results in death in a matter of minutes, because the organism literally cooks itself alive. You asked instead "without destroying the body in the process".

Also, this is not the same as producing useable energy (rather the opposite: all energy goes away as heat). The latter would require muscular activity, so you might maybe found some estimates in medical papers on malignant hyperthermia.

According to this link, cyclist Chris Hoy could blast 2500W of mechanical power during a short time.

Assuming a 30% muscular efficiency, that's 8333W metabolized.

Obviously, Hafþór Björnsson can do much better

This does not exactly answer your question, but that's a lower bound

Note: As your question implies some level of magic in the metabolism, I focused on the idea of the maximum Energy a human can make without destroying the body in the process. Of course, such an effort can not be sustained for many reasons.
You explicitaly told us not to care about overheating and waste management, but oxygen (as detailled by AlexP) and glucose flux are the next limitation in realistic biology

For the purpose of this question, don't worry about waste products or waste heat. I'll ask about those separately.

I have no data on how fast human temperature can go up and down, only the anecdotal evidence that fast temperature changes due to fever (going either up due to sickness or down due to antipyretic) usually take no less than an hour to happen.

I do have a link to a question in chemistry.se stating that the specific heat for the human body is 3.5kJ/kgK. So for a 100kg person to go from 36C to 40C in 1h, that is an energy expenditure of 1,400kJ. Over 3,600 seconds, that is ~389 watts.

That is enough to power maybe a couple 60" TV's, or seven laptops. Not enough to power a coffee maker machine, though, so I wouldn't even bother. If I'm using magic to get energy from people I'd rather mix pyromancy with necromancy - completely burning a person yelds 1kWh/kg, which is 3,600,000 joules/Kg. If a 100kg person takes an hour to completely roast, that's 360,000,000 joules in one hour, so 100kW - three orders of magnitude more power!

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To be clear: this is energy coming from all cells, just wasting energy generating heat. Muscles contracting can reach higher watt counts. See Madlozoz's answer.