How to chose which formula to use for thermal energy?

In some cases we use (3/2)kt in some cases kt and some cases (1/2)kt. How to chose which formula to use for thermal energy?

Thermal energy is distributed evenly at the amount of $$\frac 12 kT$$ per degree of freedom of the dynamical system you're dealing with.
In particular, you very often use this to calculate the thermal energy held in the velocity of a particle in a gas, which comprises three independent degrees of freedom - the three components of the velocity. This multiplies the $$\frac 12 kT$$ by $$3$$ to give $$\frac 32 kT$$.