Cochlear-implant (CI) users rely heavily on temporal envelope cues for speech understanding. This study examined whether their sensitivity to temporal cues in word segments is affected when the words are preceded by non-informative carrier sentences. Thirteen adult CI users performed phonemic categorization tasks that present primarily temporally based word contrasts: Buy-Pie contrast with word-initial stop of varying voice-onset time (VOT), and Dish-Ditch contrast with varying silent intervals preceding the word-final fricative. These words were presented in isolation or were preceded by carrier stimuli including a sentence, a sentence-envelope-modulated noise, or an unmodulated speech-shaped noise. While participants were able to categorize both word contrasts, stimulus context effects were observed primarily for the Buy-Pie contrast, such that participants reported more "Buy" responses for words with longer VOTs in conditions with carrier stimuli than in isolation. The two non-speech carrier stimuli yielded similar or even greater context effects than sentences. The context effects disappeared when target words were delayed from the carrier stimuli for ≥75 ms. These results suggest that stimulus contexts affect auditory temporal processing in CI users but the context effects appear to be cue-specific. The context effects may be governed by general auditory processes, not those specific to speech processing.