With instrumentation across the globe at naval timekeeping stations of the various European empires - much of which persisted for a hundred years and thus overlapped with later instruments and broader coverage which allowed for levelling and blending.

It's essentially a "construct your baseline" problem faced in many domains, the Fifth and other IPCC reports:

    This IPCC Special Report on Global Warming of 1.5°C uses the reference period 1850–1900 to represent pre-industrial temperature.

    This is the earliest period with near-global observations and is the reference period used as an approximation of preindustrial temperatures in the IPCC Fifth Assessment Report.

 ~ IPCC FAQ: https://www.ipcc.ch/site/assets/uploads/sites/2/2018/12/SR15_FAQ_Low_Res.pdf

and naturally there are many papers that consider alternate baselines, data quality, proxies, etc. eg:

Estimating Changes in Global Temperature since the Preindustrial Period (2017)

https://journals.ametsoc.org/view/journals/bams/98/9/bams-d-...

^^ Discussed in brief: https://www.climate-lab-book.ac.uk/2017/defining-pre-industr...

With help from sea sponges as recently discussed in https://news.ycombinator.com/item?id=39268387

There are things called 'proxies'. The same way you can assess the crime rate of a certain area by the amount of littering by the side of the road.