I recently encountered the following chart as part of an argument that CO2 does not affect global temperatures. It instantly raised my suspicions because the temperature data is just too clean--I can't believe that global temperatures is almost always one of two values, 12 degrees or 22 degrees, and that there is no noise in the measurements.

Note that this chart implies that the current temperature is about 12 degrees Celsius.

I looked into this phenomenon a little more, and came away satisfied that the above cartoon was basically accurate--the dinosaurs lived on a hotter planet than we do, and CO2 is not the main determinant of temperatures over the course of hundreds of millions of years (solar activity has changed a lot, among other things).

Still, I could swear that I've seen data showing a strong correlation between CO2 and temperature. Turns out that CO2 and temperature do have a strong correlation on the scale of hundreds of thousands of years.

The data on this chart wouldn't even show up as a blip on the previous chart because the time-scale is too short-- but the temperature swings by 10 degrees over the course of just tens of thousands of years. So what temperature is being displayed in the first chart? Is it the temperature from the ice ages, or the temperature from the modern interglacial period? If 12 degrees refers to the ice ages, then the modern global temperature is ~20 degrees C.

So what is the current global temperature?

Notice that this chart refers to a "temperature change", not an absolute temperature. That's annoying. You'll also often see "global temperature anomaly", which is basically the same thing. Nobody wants to say what the temperature is!

So I look some more, and I find that some wise guys (i.e. mathematicians) claim that there is no such thing as a global temperature! The argument seems sound, but the author goes astray when he claims that this invalidates the entire idea of "global warming". The problem is that he doesn't seem to understand how climatologists are interpreting the temperature data to arrive at conclusions of global warming*. As I pointed out above, they never actually calculate a global temperature. Instead, they use temperature anomalies, for much the same reason that this mathematician argued that there is no absolute global temperature:

Why use temperature anomalies (departure from average) and not absolute temperature measurements?

Absolute estimates of global average surface temperature are
difficult to compile for several reasons. Some regions have few
temperature measurement stations (e.g., the Sahara Desert) and
interpolation must be made over large, data-sparse regions. In
mountainous areas, most observations come from the inhabited valleys,
so the effect of elevation
on a region’s average temperature must be considered as well. For
example, a summer month over an area may be cooler than average, both
at a mountain top and in a nearby valley, but the absolute temperatures
will be quite different at the two locations. The use of anomalies in
this case will show that temperatures for both locations were below

Using reference values computed on smaller [more local] scales over
the same time period establishes a baseline from which anomalies are
calculated. This effectively normalizes the data so they can be
compared and combined to more accurately represent temperature patterns
with respect to what is normal for different places within a region.

For these reasons, large-area summaries incorporate anomalies, not
the temperature itself. Anomalies more accurately describe climate
variability over larger areas than absolute temperatures do, and they
give a frame of reference that allows more meaningful comparisons
between locations and more accurate calculations of temperature trends.

So in the end, my question had no answer. There is no global temperature.

*the mathematician also grossly misinterpreted one of their cited articles about how global warming is connected to amphibian extinctions (this is the only article I looked into, because I have some familiarity with the topic)