Appropriacy is the paramount consideration of such an inherently polite speech act as thanking in its use. Traditional study of thanking focuses more on the quantitative investigation of its diverse forms and functions than on interpretation of the process in which it is used appropriately and adequately or not among English native or nonnative speakers. This paper particularly explores how to make the speech act of thanking appropriate and acceptable in dynamic context from the perspective of Chinese EFL learners who tend to respond in mute English or Chinglish in cross-culture thanking situation through analysis of the spoken discourse based on cognitive and cultural comparative approach. It contents that in foreign language learning environment, L2 contextual knowledge also comes into compensation for the lack of authentic context compatible with L2 use in the diachronic process of EFL learning as L1 contextual knowledge does. In a specific communicative situation, the learner has to manipulate his contextual cognition consciously and make an appropriate choice among linguistic or strategic forms activated by the two types of contextual knowledge stored in memory. The choice-making needs considering adaptation to dynamic context like the objects of gratitude, the benefactor's psychological state and the communicative social context as the most important parameters. Only in that way is appropriacy of thanking possible in cross-cultural communication.