You say interpolation is incredibly unreliable ... except for the studies and published papers that show it is reliable.
If your back yard is warmer than your front yard in the morning and cooler in the afternoon during common weather in the summer then if analysis/observation shows that is a reliable pattern you are justified in saying lets head to the back yard, it'll be cooler, because it is on this sort of day. That is the sort of pattern that interpolation is identifying and using.
And the proxy readings that I commented on and that were discussed in the link I provided were not proxy readings from 500 years ago. They were available proxy readings that overlap the instrument temperature period and included areas where we had instrument coverage gaps. It pays not to comment on or dismiss something you haven;t read.
It's fine to question. But not fine to do so and just get the facts wrong. That suggests bias and predetermination.
And repeating, we have 7,000+ long term station locations covering most of the globe that provide temperature records that show warming consistent with CO2 impacts. The gaps in the coverage aren't an issue.
