Yes, temperature is a vector.
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Heat is energy. It and temperature are both scalars.
Force, velocity, acceleration, and displacement are vectors. Mass, temperature, time, cost, and speed are scalars (not vectors).
Yes, a vector can be represented in terms of a unit vector which is in the same direction as the vector. it will be the unit vector in the direction of the vector times the magnitude of the vector.
-- dollars -- weeks -- kilograms -- degrees (of temperature) -- pages -- watts -- decibels -- joules -- lumens
The zero vector is both parallel and perpendicular to any other vector. V.0 = 0 means zero vector is perpendicular to V and Vx0 = 0 means zero vector is parallel to V.