Easy - if global temperature is a meaningful concept, it is global.
Global temperature change can therefore be measured anywhere on the globe (unless and except when global factors are overwhelmed by local ones).
How do we measure human body temperature change?
Easy - just do repeated measurements anywhere on or in the human body: the rectum, mouth, armpit, forehead - all give valid measurements of global body temperature changes.
This is done everyday in hospitals and homes all over the world, and it works fine so long as the serially repeated measurements are made in the same place (e.g. if you start by measuring forehead temperature then switched to rectal temperature, the temperature measurement will rise - even when the persons global temperature stays the same - because the rectum is warmer than the forehead).
And of course local factors can overwhelm global - if the forehead to sponged with icy water just before taking a reading, or if the armpit has a hot water bottle applied.
Global planetary temperature trends can *easily* and validly be measured anywhere on the globe with equal validity - so long as the global trends are not overwhelmed by the local changes (building a city around the temperature station, building an air conditioning vent blowing onto the thermometer etc.).
This is not rocket science, a kid can measure temperature trends in a single place, indeed kids have done it.
Alternatively we could examine the history or study the archeology of a single place to give a bigger time frame of temperature trends.
The process yields a graph - a kid could plot it.
So what do the computer models of professional climate 'scientists' add to this?
Merely incompetence, vested interests and dishonesty; related to their absurd and utterly unfounded claim to be able to predict the future...
There is a criterion reference for 'true' human body temperature - core temperature, inside the body, usually the peritoneum - against which other temperatures (oral, armpit etc.) can be validated.
But there is no criterion reference for *the* temperature of the earth: it is an arbitrary statistical construct.
In reality, there is no global temperature of the earth - there are only the temperatures of specific parts of the earth.
Various temperatures from around the earth can be averaged together, but the selection of these readings, and their weighting in the average, is essentially arbitrary (unless, perhaps, the constructed average could be validated by using it to make predictions, and these predictions then coming true. Needless to say, true predictions ought to concern the future, or at least independent and previously un-analyzed data.)
And true global temperature change is therefore the *change* in temperature (its trend) observed at any and every place on the earth (except when local change has been overwhelmed by local factors) - there just is no non-arbitrary way of sampling, summing or averaging these individual temperature measurements done in specific places.
I repeat: There is no non-arbitrary way of averaging temperatures from different parts of earth because there is no criterion reference for the 'true' 'global' temperature.
Indeed, it is the fact that the summary statistic supposed to represent the temperature of 'the earth' is actually a non-valid construct, which has enabled the 'anthropogenic global warming' scam.
Otherwise the notion would have been easily refuted by the observation of a single contradictory trend (which could not be explained-away by local factors) - e.g. the Medieval warm period. One such trend is a refutation - but in fact there are several.
It is purely because of the manipulable nature of the process of creating an (arbitrary) single summary statistic for global temperature that the AGW/ climate change nonsense has been able to evade refutation.
As so often, sheer dumb incompetence (the product of micro-speclialization in research - 'research', not science) combines with indifference to reality, to generate a power and wealth grab.