If you can measure the input energy (Sun's spectrum) and compare it to the reflected energy ~30% (Earth's reflected spectrum) you can compute the absorbed energy ~70% (planet's absorption). Isolating that absorbed energy to just the surface requires some approximations and a lot of instrument calibration.
The sun (in space) has a spectrum of a black body at ~5700 K.
When this energy hits the atmosphere, some is reflected (called Albedo) and some is absorbed and later radiated out again at a different frequency as heat (measured by IR Spectroradiometers).
The atmosphere is quite cool compared to the surface of the earth and it doesn't have a lot of mass for heating directly, but it is good at catching the longer wave heat infrared (IR). So when the surface of the earth is measured from space about 50% of the IR (heat) energy passes through the clouds and 50% is reflected back (green house effect).
By comparing the sun's input, to the measured albedo they can correct for some of that effect. It can also be calibrated against sensors on the ground which show what amount of energy makes it through the atmosphere. Notice that $H_2O$, $O_3$ (ozone), $CO_2$ and $O_2$ absorb noticeable amounts of the radiated energy (absorption bands). In this image the yellow represents the spectrum outside the atmosphere like in the image above, with the red showing what frequencies and power strength reach the surface at sea-level. Note how $O_3$ absorbs the higher frequency (shorter wave-length) ultra-violet and keeps us from getting too sun burnt?
So the IR radiation from space can be measured and compared to the model and ground based sensors. This image is a broad-spectrum interpretation of what the "brightness" or power would look like if we could see in this frequency band. This isn't a spectrum view but rather a view of the total amount of energy seen reflected using very wide IR vision. The wide vision makes seeing details difficult as you can see there are mostly big blobs of different strengths of reflected IR power. This is where NASA's camera is much more powerful because of a combination of filters and frequency resolution they can increase the dynamic range of the image dramatically and see much more than blobs (see the detail in the Lut Desert image below).
Where the current model which is always being refined by new information looks something like this.
The specific instrument that NASA uses is called Moderate Resolution Imaging Spectroradiometer (MODIS) and there is an entire team to support calibration. The MODIS instrument has 36 different spectral bands (groups of wavelengths), including some that detect thermal radiance, or the amount of infrared energy emitted by the land surface. Since the two MODIS instruments scan the entire surface each day, they provide a complete picture of earthly temperatures and fill in the gaps between the world’s weather stations—particularly in extreme environments where temperatures are simply not measured.
The spectral band separation for the 36 MODIS bands is based on a
complex system of dichroic beamsplitters, focal plane masks,and
individual bandpass filters. There are four co-registered focal planes
separated by three dichroic beamsplitters to cover the VIS (400 nm to
550 nm), NIR (650 nm to 950 nm), SWIR (1200 nm to 2250 nm), MWIR (3600
nm to 4600 nm) and LWIR (6500 nm to 14500 nm). Linear detector arrays,
one for each band, are covered by bandpass filters of dimensions as
small as 1 mm by 7 mm. The MODIS requirements include relative
bandwidths as small as 1%, with tight tolerances on band center, band
width, edge slopes, and out-of-band specifications. -- IEEE
VIS -- Visual Spectrum, NIR - Near InfraRed, SWIR - short wave infrared, MWIR - medium wave infrared, LWIR - long wave infrared.
The advantage of the MODIS sensor is most of the atmospheric temperatures are much lower than the surface of the earth. So using narrower IR filters and comparing different bands the near direct temperature of the earth's skin can be measured (assuming proper calibration). Using this information directly they can make daily direct measurements. For example the Lut Desert was found to often be the hottest spot on the planet:
The Lut Desert has an areal extent of about 80,000 km and contains several odd geomorphic distinctions making it a unique place. Large areas of the Lut Desert regularly exceed 65.0°C, and the hottest spot on Earth was detected in the Lut five out of seven years.
IR imaging in general is often used in industrial applications to find irregular sources of heat. It can be used to see objects in great detail where each pixel acts as a tiny thermometer allowing you to measure the temperature of every pixel on an image. This is how the MODIS works, but it is much more complicated. Here is an example from a FLIR handheld device illustrating the concept with the LEFT image in black and white with the reference spot highlighted, compared to the RIGHT image in IR with the same spot highlighted.