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Heat is energy in the form of vibration of atoms in a matrix (solids), the movement of atoms in a fluid, or electromagnetic radiation. There are 4 ways for heat to travel, respectively.

In solids: Vibrating atoms or molecules vibrate the next one along like a vibration on a stretched string. This is called conduction. Its not affected by gravity. This is why a radiator is hot when it is filled with hot water.

In fluids: Atoms/molecules move more quickly and therefore occupy more space. Therefore the same weight of stuff takes a larger space. Given a fluid that has an even pressure, the lighter bits rise to the top, because the heavier bits sink. This is called convection. This is affected by gravity. Also, the speeding molecules can mix with the other slow ones. This is called diffusion. This is not affected by gravity.

In a transparent medium (eg, air or a vacuum) electromagnetic radiation travels through the medium, and can make atoms and molecules start wiggling if they absorb the radiation. This is called radiation. It is not affected by gravity.

If you were in the space station, in air but no gravity, then heat would spread out in all directions, via all 4 mechanisms except convection. If you had no air, then its conduction and radiation only. If the hot and cold bits are not touching, then its radiation only.