Analysis of Shot Noise at Finite Temperatures in Fractional Quantum Hall Edge States

We investigate shot noise at {\it finite temperatures} induced by the quasi-particle tunneling between fractional quantum Hall (FQH) edge states. The resulting Fano factor has the peak structure at a certain bias voltage. Such a structure indicates that quasi-particles are weakly {\it glued} due to thermal fluctuation. We show that the effect makes it possible to probe the difference of statistics between $\nu =1\mathrm{/}5,2\mathrm{/}5$ FQH states where quasi-particles have the same unit charge.Finally we propose a way to indirectly obtain statistical angle in hierarchical FQH states.