Extracting appropriate custom instructions is an important phase for implementing an application on an extensible processor with a reconfigurable functional unit (RFU). Custom instructions (CIs) are usually extracted from critical portions of applications. It may not be possible to meet all of the RFU constraints when CIs are generated. This paper addresses the generation of mappable CIs on an RFU. In this paper, our proposed RFU architecture for an adaptive dynamic extensible processor is described. Then, an integrated framework for temporal partitioning and mapping is presented to partition and map the CIs on RFU. In this framework, two mapping aware temporal partitioning algorithms are used to generate CIs. Temporal partitioning iterates and modifies partitions incrementally to generate CIs. Using this framework brings about more speedup for the extensible processor.