Discuss a heat capacity of a two-levels system

Question

Discuss the below:

Heat Capacity of a two-levels system.

Q: Consider a 2-level system with an energy splitting between the upper and lower level. Using Boltzmann statistics, show that the heat capacity of the 2-level system equals:

C=∂U/∂T=k_B((Δ/T)² e^Δ/T)/(1+e^Δ/T)^₂

What happens in the limit of ΔT<<1