How much heat was released from the 2019-2020 Australian bush fires?
Right. We can make some estimates of the scale of the problem, but they will come with a healthy margin of error.


If we assume that wood has a calorific value of 18.5 GJ/t (from the phyllis2 database)
The area burned is 18.6 Mha (from Wikipedia here)
The standing volume of material is circa 1500 m3/ha (an educated guess based on Eucalyptus values in Forest Yield)
The density of timber is circa 0.5t per dry m3 (from Forest mensuration handbook)
and only 90% of that material actually burns (a guess)


Then:

There's around 675 tonnes of material burned per ha releasing 12,150 GJ of energy which is equal to 225,990,000 TJ for the total area or 3,587,143 Hiroshima bombs (at 63 TJ each)...

This is a (very) rough calculation, but it gives a scale of the amount of heat released. This is about 10 day's worth of solar constant radiation over the same area, so it might appear in local temperature readings, but bear in mind that 1) there was already unusually high temperatures in the area, and 2) fires like this produce a lot of smoke which will have had an effect on the local radiation budget.

In terms of all that CO2, you can expect it to be reabsorbed by the surrounding biosphere which is described in the impulse response function described in the IPCC AR5 WG1 CH8 technical supplement (8.SM.11.1 Equations for the Global Warming Potential). You can also expect the burned areas to regrow - which will absorb CO2 as well. Depending on rates of growth, I would expect this to take several decades. - but there is a lot of very complex processes, so this is open to a lot of discussion!

Hope this helps.