The hull surface is unwrapped into a flat strip running 0°–360° around the spacecraft's circumference. Every column of the strip is its own lumped thermal node solving a real energy balance each frame, exactly as the 3D version does per panel — just drawn flat instead of on a cylinder:
C·dT/dt = α·S·max(0, cos θ)
+ Q_internal/N
- ε·σ·T⁴
where S = 1361/d² W/m² is the solar constant scaled by distance d (in AU) via the inverse-square law, σ is the Stefan-Boltzmann constant, α/ε are the surface's absorptivity and emissivity, θ is the angle between that column's outward normal and the sun line (so cos θ < 0 columns are self-shadowed, on the far side of the hull), and Q_internal/N spreads the crew-and-equipment heat load evenly across every column.
- Sun-facing hot band — the column pointed straight at the sun (θ = 0) absorbs the full solar flux and climbs until its own blackbody radiation balances it out, often above +100°C for a dark, absorptive coating.
- Shadow-side cold band — columns past 90° from the sun receive no direct sunlight at all; with no air to convect heat around, they cool toward whatever internal heat leakage and low-level structural conduction can supply, which can be well below -100°C.
- Distance from the Sun — moving from Earth's 1 AU toward Jupiter's ~5.2 AU cuts the solar constant by the square of the distance, flattening the whole map toward the cold end.
- Barbecue roll — slowly spinning the hull (as Apollo and Soyuz crews did) sweeps the hot band around the strip over one roll period, averaging every column's exposure and shrinking the hot/cold spread instead of baking one fixed side.
Real hardware relevance: this is the same lumped-node radiative balance used to size ISS radiators, spacesuit MLI layers, and satellite thermal-control coatings.