With numerous amounts of bonfires of a large size being created and knowing that forest fires in Australia can raise the temperature of the area there, is it feasible that the temperature of the UK slightly increases on bonfire night due to the amount of bonfires that have been lit or is the increase so infinitesimally small that it couldn't be measured let alone felt by the populace?
I doubt very much if the overall land area of the UK would be affected by the presence of an arbitrary number of bonfires. I have no idea of the number of bonfires, but let's do an estimation.
The population of the UK is around 60 million people.
Assume that the people most likely to light bonfires are in the 15 to 40 age group, UK Official Population Figures, produces a guessimate of 20 percent.
So you have possibly 12 million potential firestarters, let's cut that down to 6 million actually available to light fires, and that 100 people attend the event.
So you have 6000 large bonfires, (or a lot more smaller ones, it evens out) and say the area of each bonfire base is 10 square metres. So 6000 by 10 square metres is 60,000 square metres occupied by burning material. The total land area of the UK is 243.61 billion square metres. Actually that 6,000 is way too low but even 60,000 fires would still be ok in this rough estimation.
Enough already, I think.
I am ignoring calculating the heat output of each fire. A better way to estimate, in my opinion, is to consider if an average 5 degrees Celsius of 243.61 billion square metres of air will be affected in any detectable way by 60,000 square metres at an average temperature of say 600 degrees Celsius, (the average temperature of burning wood).
No, it won't, even if my number for fires is to 60,000 fires, which looking at it now seems a more likely figure. No matter what the fire number is, it still has to contend with 244 billion square metres of 5 degree Celsius air.
In addition we may have to allow for 2 to 5 million hot car exhausts and 3 million plus domestic heating house fires, which would have far more effect than bonfires.
So locally, within an radius of 200 metres of each fire, the air temperature increase is detectable, beyond that, no chance of detection seems likely.
A better way to think about it, after the fires all go out about two in the morning, is to ask yourself, will you notice a distinct change in the weather for the next day? Will all this energy affect you?
You could find out yourself, by looking at the weather pattern over London during the 1940/3 blitz, for example.
I put this part as the real answer, because I believe that rather than saying it depends on various factors, research can be carried to establish if this idea is true, by checking on weather patterns shortly after the fires and looking for correlations.
More supporting, (but indirect) evidence is the deadly smog that regularly covered London due to domestic coal fires, but it's far too complicated as regards the number of variables to easily establish correlations between the bonfire and the weather.
The focus then moves from PhysicsSE to EarthSciencesSE, imo.