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 $\frac 32 kT$.