anotero
Autocross Champion
I agree with your investigational spirit, but I will say that the warming/expanding of the Sun is most definitely not the most significant factor causing the Earth to warm this significantly. Experts have estimated that the warming/expanding Sun has contributed to at most roughly 0.1C of the warming we've observed. The sun will gain 1% luminosity over the course of 1 billion years. It's definitely warming/expanding, but not at the rate to account for the full warming we've observed over the past century and change. Is it down to the natural swing of cold and warm periods the Earth sees? Maybe. Is it greenhouse gases and human pollution? Like you said, maybe. I think there's strong evidence that it is, but like you say, we haven't been able to definitively prove this hypothesis.
I wonder what explanation adepts of global warming/anthropogenic climate change have for the Roman climatic optimum.