It’s not a stupidly easy question. It is extremely hard. Calculating the average temperature of all molecules on Earth is extremely hard due to the vast range of temperatures across different environments, from the Earth’s core to the atmosphere. Calculation isn’t the problem but collecting data is. You need to collect all the data that distributed widely on earth. Factors like altitude, latitude, and specific conditions in different regions making collecting an accurate data even harder.

One thing that might help is knowing that the crust is very thin, 1% of the Earth’s mass. The core is 15% and the Mantle is 84%. But we don’t have to be too exact — the earth’s mantle isn’t one temperature

The Mantle ranges from 1000°C near the crust and 3700°C near the mantle. The core is starts there and gets up to 6000°C.

So, just a simple formula weighted by mass might be:

.84*((3700°C+1000°C)/2) + .15*((3700°C+6000°C)/2)

Which equals 2701.5°C. That answer might be fine for a Lemmy but an academic paper would have major error bars.

I also asked ChatGPT and Bard, out of curiosity. ChatGPT was more conservative and told me it’s hard to get anything besides a rough estimate. Bard warned about all that too but then said probably between 3000°C and 4000°C.

So, I’d say about 3000°C. My quick and dirty little formula could easily be +/- 1000°C and fall in Bard’s range.

The mean temperature of the earth is 59°(15°C). This is from NASA Science Solar System Temperatures. I don’t know if this answers your question but I gave it a shot.

I have no exact answer but the earth’s mantle makes up approximately 84% of its volume and has temperatures ranging from 500k to 4200k. So I would estimate the average temperature to be in the upper bounds of that range.