No, heat is not a vector field. Heat is a form of energy transfer due to a temperature difference, and it flows from hotter to cooler regions. The concept you're likely referring to is
heat flux, which is a vector field.
Heat flux is the rate at which heat energy flows through a surface per unit area, and it is a vector because it has both magnitude and direction. The direction of the heat flux vector is always from higher temperature to lower temperature, in line with the second law of thermodynamics.
To summarize:
- Heat itself is not a vector field. It's the energy being transferred.
- Heat flux is the vector field that describes the flow of heat in space.
If you're dealing with the flow of heat, you'll likely be using the concept of heat flux, which is a vector.