  Interplay of cotunneling and single-electron tunneling in a thermally
isolated single-electron transistor (SET) leads to peculiar overheating
effects. In particular, there is an interesting crossover interval where the
competition between cotunneling and single-electron tunneling changes to the
dominance of the latter. In this interval, the current exhibits anomalous
sensitivity to the effective electron temperature of the transistor island and
its fluctuations. We present a detailed study of the current and temperature
fluctuations at this interesting point. The methods implemented allow for a
complete characterization of the distribution of the fluctuating quantities,
well beyond the Gaussian approximation. We reveal and explore the parameter
range where, for sufficiently small transistor islands, the current
fluctuations become gigantic. In this regime, the optimal value of the current,
its expectation value, and its standard deviation differ from each other by
parametrically large factors. This situation is unique for transport in
nanostructures and for electron transport in general. The origin of this
spectacular effect is the exponential sensitivity of the current to the
fluctuating effective temperature.
