Focused ion beam processing of low melting materials, such as polymers or biological samples, often leads to chemical and morphological instabilities which prevent the straight-forward application of this versatile direct-write structuring method. In this study the behaviour of different polymer classes under ion beam exposure is investigated using different patterning parameters and strategies with the aim of (i) correlating local temperatures with the polymers' chemistry and its morphological consequences; and (ii) finding a way of processing sensitive polymers with lowest chemical degradation while maintaining structuring times. It is found that during processing of polymers three temperature regimes can be observed: (1) at low temperatures all polymers investigated show stable chemical and morphological behaviour; (2) very high temperatures lead to strong chemical degradation which entails unpredictable morphologies; and (3) in the intermediate temperature regime the behaviour is found to be strongly material dependent. A detailed look reveals that polymers which rather cross-link in the proximity of the beam show stable morphologies in this intermediate regime, while polymers that rather undergo chain scission show tendencies to develop a creeping phase, where material follows the ion beam movement leading to instable and unpredictable morphologies. Finally a simple, alternative patterning strategy is suggested, which allows stable processing conditions with lowest chemical damage even for challenging polymers undergoing chain scission.