Isn't the planet cooling down?

Quite true, but that should not detract from the fact that the earth’s average global surface temperature is incontrovertibly warmer than at any time in the past 2000 years (and almost certainly very much longer, but paleoclimate data becomes less accurate the farther back you go). In particular, the average global temperature now is significantly warmer than in the so-called Medieval Warm Period, mainly because of the accumulation of post-industrial GHG emissions.

Is it? At that time, there was a climate that allowed (marginal) agricultural activity in southern Greenland coastal areas for a century or two, and from what I’ve seen on the news, we are only just now getting to that point again for Greenland. Or was the weather pattern different back then?

The heat emmission of the planet can be judged the same as for any warm object - how much heat is coming off? (Had this discussion over heat loss from the hot water tank. Go down to your hot water tank, put your hand on it - how warm to the touch is it?)

in some places, heat is coming out of the earth as molten rock or old, faithful geysers. In other areas, permafrost exists, the ground is forever frozen (minus a bit of sun-induced global warming) and in “recent” times we’ve had whole sheets of ice covering fairly low latitudes. So heat conduction is obviously pretty minimal. The implication is that not much heat is escaping, but some is.

The evidence shows that the Medieval Warm Period was largely a regional phenomenon, not a global one, occurring in some parts of the Northern Hemisphere and notably absent in the Southern. Evidence for the unprecedented extent of truly global post-industrial warming was one of the major contributions to the paleoclimate chronology by Mann et al:

A timely new article reports that the oceans contained a record high amount of heat in 2021. This is the sixth year in a row that the oceans have set a new record heat level.

The scientific article says the oceans contain 14\pm11 zetajoules or 16\pm10 ZJ more energy than last year, depending on which dataset is used. The linked below popular press article says that’s the equivalent heat of 2.20752 \times 10^8 Little Boy atomic bombs.

So yeah, getting warmer.

"The total mass of Earth’s atmosphere is about 5.5 quadrillion tons, or roughly one millionth of Earth’s mass. " - How Much Does Earth’s Atmosphere Weigh? | Britannica

Global Warming largely addresses only this one millionth of Earth’s mass.

Even all water on earth combined is 0.05% of the Earth’s mass. The Earth has lost a quarter of its water.

And because green house gases prevent heat from the atmosphere from radiating back into space, the heat is primarily being absorbed by the oceans. The article below says that 90% of the trapped heat due to anthropogenic climate change is in the oceans.

Although not totally accepted, signs point to two periods where everything was ice-covered (snowball Earth), 2100 and 650 Mya when presumably the radiogenic heat mentioned in MrDibble’s link would be greater than the more recent glaciation periods

Moderator Note

Let’s all keep in mind that this is not a general discussion of climate change. Some discussion is relevant, as the OP did ask later in the thread about measuring the Earth’s temperature from several hundred million miles away, which would end up measuring the Earth’s surface temperature.

However, the OP is about the overall temperature of the Earth, not the temperature of the Earth’s surface or atmosphere. Let’s not get sidetracked into a general discussion of climate change as that is a topic for a different thread.

In my news today, a mew study indicates that the Earth’s interior may be cooling faster than expected. New laboratory measurements of the type of material found at the boundary between the core and the mantle found that this material has a higher thermal conductivity than previously thought. This is significant because there is a rather substantial heat differential between the core and mantle, so this boundary layer could be conducting heat out of the core at a much higher rate than previously predicted.

Excellent. Thank you. This actually does answer my question. Yes, the earth is cooling down. (And thanks for reorienting the nature of the posts.)

Most of the mass or volume of the Earth is cooling, with only a small portion at the surface heating up. But the part that’s heating up is heating up much quicker than the part that’s cooling down.

By 5 orders of magnitude.

The mantle is cooling at a rate of about 1 deg in 5 million years.
https://www.sciencenews.org/article/earth-mantle-cooling-faster-expected

The surface has warmed about 1 deg in the last 50 years.
Climate Change: Global Temperature | NOAA Climate.gov

So absent careful explanation of what you’re talking about, I would say this assertion is somewhere between “wrong” and “highly misleading”.