Vessels continously gain Heat from the nearest star based on the following factors:

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Exterior Heat Factor (Inhabited Parts)

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Distance from its star.
Whether or not the part is exposed to sunlight.
Whether or not the part is insulated (75% reduction).

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Exterior Heat Factor (Uninhabited Parts)

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Number of parts in the vessel without an atmosphere (Probably a good idea to ignore very small parts, and things like pipes).
Whether or not the vessel is exposed to sunlight.
Distance from its star.

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Total Heat Gain for the vessel is based on the sum of all parts\' Heat Factors. This is applied as the Heat resource to inhabited parts, which goes towards their Thermal Load.

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Because distance to a star determines heat gained, travelling extremely close to one will require an absurd amount of radiators, eventually becoming impractical to the point of ridiculousness.

Kerbstar Comprehensive Life Support System (KCLSS)