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We provide an experimental demonstration that the focusing of ionic currentsin a micron size hole connecting two chambers can produce local temperatureincreases of up to $100^\circ$ C with gradients as large as $1^\circ$ K$\mum^{-1}$. We find a good agreement between the measured temperature profiles anda finite elements-based numerical calculation. We show how the thermalgradients can be used to measure the full melting profile of DNA duplexeswithin a region of 40 $\mu$m. The possibility to produce even larger gradientsusing sub-micron pores is discussed.

Localized Joule heating produced by ion current focusing through micron-size holes