Earth's thermosphere, which consists of both the ionosphere and the exosphere, feels cold because of the low density of air at that level. Measurements of air temperature reveal how energetic the measured particles are, but with so few particles, the thermosphere is unable to effectively transfer heat.
Heat may be transferred by direct contact between two surfaces, by convection from one surface to another or by radiation. Earth's thermosphere, which begins at around 50 miles above Earth's surface and extends to almost 400 miles, has such a low density of air molecules that very few can ever be in direct contact with a surface at any given time, limiting the potential for heat transfer. Energetic particles in the thermosphere do radiate heat, but the very low density of particles limits the amount of energy available to the zone as a whole, so the radiation remains relatively weak.
While the thermosphere is cold on the relatively large scale of a human body, the particles in the region can absorb high amounts of energy, which registers as heat when measured. Temperatures in excess of 1,800 degrees Fahrenheit have been observed among single particles, but the general lack of material at this altitude means very few particles are available to transfer this energy.