How big is a 1kW fire? What is the size/scale of a wood fire that is producing 1kW?
I'd like to improve my ability to conceptualize various power scales.
 A: Let's work this out from the Stephan Boltzmann law. What color is a fire? If you look at color charts for black body radiators at various temperatures, I estimate it to be about 1000K. (Be careful: some flames are colored by strong emission spectra, making their light very different from a blackbody radiator's color). Glancing around the web from various sources tells me that between 1000K and 2000K is right.
The Stefan Boltzmann law then tells me that a blackbody radiator at 1500K throws out about $300\,{\rm kW\,m^{-2}}$, so this implies a flame of the order of $3\times 10^{-3}{\rm m^2}$: the size of a small gas ring campstove. From my answer here I estimate that about 20% of the energy let slip by burning is through radiation: the rest is through hot gasses. So we need to scale our answer down further: about a bunsen burner flame.
Let's check this: Wikipedia gives me a heat of combustion for propane of $–2202.0\,{\rm kJ\,mol^{-1}}$, so $2\,{\rm MJ}$ for about 20 liters of gas at room temperature and pressure. My bunsen burner manual says it uses about 100 liters an hour. Thats $2\,{\rm J}$ for $3600/5$ seconds, or about $2.5\,\rm kW$.
So it's a bunsen burner working slowly.
A: Cooking oil contains around 9 kcal per gram and is 930 grams per litre.
When you do the conversions, it works out to 9.75 kilowatt hours in a litre bottle of cooking oil. So it's a fire that will burn a bottle of cooking oil in 9 and three quarter hours. This is actually quite a small fire compared to what you may be used to lighting in a fire place. It really shows how much you lose up a chimney having to get rid of the fumes. You could probably make this fire in a vented 400 gram tin can (like what you use for beans, soup or cat food) with a few flames up to the top of the can. I used to have a forced air wood gas stove around 6 inches tall and wide, and it claimed to have an output of about 3 kilowatts.
Alternatively it's about 30 tea lights.
Experiment: Cut the bottoms off some drinks cans. Drill 4 holes (3mm bit) around the bottom rim where the can stands. Poke cotton wool through the holes and moisten with cooking oil. See how many assemblies it takes to have a burn rate of about 100g/hour with cooking oil. You can do this indoors (away from flammable materials!) as the flames are low in soot (which also helps convert almost all of the oil's energy to heat).
Float the assembly in oil and light the wicks. See how many
A: most fires do not burn steadily. the heat release rate ramps up, peaks,  and then drops down. a well established experimental correlation in fire science shows that the mean flame height ($L$) divided by the effective diameter ($D$) of the fuel source  is proportional to the heat release rate ($Q$) to the 0.4 power. The correlation does well for large fires but doesn't do as well for smaller fires or for mass fires (when $L/D < 1$). For typical fuels, under atmospheric conditions:
$L = -1.02 D + 0.235 Q^{0.4}$ ($D$, $L$ in $\rm m$; with $Q$ in $\rm kW > 0.8\,kW$). So, for a $1\,\rm kW$ round pile of wood $10\,\rm cm$ wide, $L\simeq14\rm\, cm$. Alternatively, $Q = [(L+1.02D)/0.235]^{2.5}$, so if $L$ and $D$ are known, $Q$ can be estimated.
