We study subcritical fracture driven by thermally activated damage accumulation in the framework of fiber bundle models. We show that in the presence of stress inhomogeneities, thermally activated cracking results in an anomalous size effect; i.e., the average lifetime tf decreases as a power law of the system size tf ∼L-z, where the exponent z depends on the external load σ and on the temperature T in the form z∼f(σ/T3/2). We propose a modified form of the Arrhenius law which provides a comprehensive description of thermally activated breakdown. Thermal fluctuations trigger bursts of breakings which have a power law size distribution. © 2008 The American Physical Society.