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Thermally assisted switching of submicrometer magnetic tunnel junctions is investigated. It is found that writing can be done with pulses of the order of 1 ns. Switching current and switching current jitter are seen as strong functions of temperature, whereas both are only weakly dependent on current pulse duration. Micromagnetic modeling using a stochastic Landau-Lifschitz equation is used to understand thermal effects. The simulation predicts the observed switching current but does not explain the magnitude of the switching current jitter.