We can at least talk about the temperature of the surface of Mercury. There's no atmosphere so we can't talk about the air temperature, and the temperature that an object (space suit, lander) would feel is affected by radiative heating from the hot rocks and any residual sunlight, and by the object radiatively cooling out into space and that requires a detailed model.
It is going to be complicated by the fact that Mercury's surface is quite rough from billions of years of pummeling by meteors and its own, earlier volcanic activity. That means one side of a crater or a peak will be getting hot in sunlight while the opposite side will still be in darkness and quite cold.
So I think as you zoom in, your diagram will start showing all kinds of hot spots in the cold region, and cold spots in the hot region due to topography. That' region is probably going to be tens of kilometers wide, but it depends a lot on the topographical details of each region.
During the recent total eclipse of the Sun, NASA flew jets with telescopes high above much of the water in the atmosphere in order to make thermal infrared images of the planet Mercury!
From Chasing the Great American 2017 Total Solar Eclipse: Coronal Results from
NASA's WB-57F High-Altitude Research Aircraft:
Observing during the eclipse with the WB-57s allowed us to also do some interdisciplinary “bonus” science. Mercury is the closest planet to the Sun and never very far from it in the sky, making it difficult to observe – during the day, the bright sky presents a significant background and equipment must be able to deal with bright sunlight, while observations at twilight (before sunrise, after sunset) are at very low elevation, through multiple airmasses, and thus complicated by significant seeing. At ”thermal” near-infrared (NIR) wavelengths of 3–5 μm, this is a particular problem since atmospheric emission and absorption are that much worse. During the eclipse, the sky is significantly darker (even during partiality) and Mercury is near zenith, providing vastly improved observing conditions.
NIR observations at 3–5 μm probe the temperature of Mercury’s regolith down to depths of a few cm. The cooling timescale of the regolith is poorly known, but is a strong function of the soil composition and density/porosity. MESSENGER X-ray fluoroscopy measurements probed composition only in the top few microns; composition and density below this thin layer are unknown. Measuring the temperature as a function of Mercury local time would reveal the diurnal cooling timescale and, along with modeling, constrain regolith composition and density/porosity to few-cm depths. In turn, this provides insight into how Mercury’s regolith was processed during early planetary formation and bombardment, improving our understanding of rocky planet formation during the early solar system. There are no existing spatially-resolved NIR measurements of Mercury; we attempted to make the first “heat map” of Mercury with the WB-57.