In this note we study the "conformal limit" of the TBA equations which
describe the geometry of the moduli space of four-dimensional N=2 gauge
theories compactified on a circle. We argue that the resulting conformal TBA
equations describe a generalization of the oper submanifold in the space of
complex flat connections on a Riemann surface. In particular, the conformal TBA
equations for theories in the A1 class produce solutions of the Schr\"odinger
equation with a rational potential.