If you cannot step 10 years to determine a 30 year trend, how can you step 30 years for a 100 year trend? And what does a 100 year trend mean for a planet that has seen climate change over 100,000 year periods? How can you step 100 years to determine a 1000 year trend?
And what would make anyone think we know the average temperature of the entire earth for the year 1812? Or 1513? To within 1-2 degrees? That is hubris.
No need for steps. The satellite 32 year trend is 1-2C per century. The lower end may be more accurate since El Chichon hit in 1982 after satellites started measuring global temp in 1979. The glut of El Nino conditions during the 80's and 90's appears to have caused diminished outgoing long wave globally (due to clouds??) and thus some global warming. There were lots of local variations and various natural cycles and quasi-cycles during the 32 years, but not enough natural change to affect the 1C per century average (e.g. the sun did not increase its radiation that much, etc)
But the bottom line is that the best explanation of 1C rise per century over that time period is CO2. I realize there is some dispute over the role of CO2 and I have read most of the alternatives. But those fall into a small percentage of scientists. What follows from recognition that CO2 may cause a rise of 1C per century is that there is no long term positive feedback; weather will do it's own thing, driven by solar, and may provide subtractions or additions to global warming. There is some evidence for negative feedback, strong and more frequent storms, increased water cycle, etc. But the Arctic will not "melt" in the next century or even a few centuries even if CO2 keeps increasing, due to diminishing returns on CO2 warming.
A GOOGLE for "p value add statistical significance" will return many explanations, including how significance is affected by sample size.