We study the WKB periods for third order ordinary differential equation (ODE) with polynomial potential, which is obtained by Nekrasov-Shatashvili limit of ($A_2,A_N$) Argyres-Douglas theory in Omega background. In minimal chamber moduli space, we derive Y-system and thermodynamic Bethe ansatz (TBA) equations using ODE/IM correspondence. The exact are identified Y-functions. Varying parameters ...