  Motivated by the method of self-similar variables for the study of the large
time behavior of the heat equation in twisted wave-guides whose non circular
cross-section and the support of twisting diminushing simutaneously to zero.
Since in this limit the strength of the twisting increases to infinity and its
support shrinks to the point, we show that the corresponding Schr\"odinger
operator converges in a suitable norm-resolvent sense to a one-dimensional
harmonic oscillator on the reference line of the wave-guide, subject to some
extra Dirichlet boundary condition at the twisting point support.
