Transferring linguistic knowledge from a pretrained language model (PLM) to an acoustic model has been shown to greatly improve the performance of automatic speech recognition (ASR). However, due to the heterogeneous feature distributions in cross-modalities, designing an effective model for feature alignment and knowledge transfer between linguistic and acoustic sequences remains a challenging task. Optimal transport (OT), which efficiently measures probability distribution discrepancies, holds great potential for aligning and transferring knowledge between acoustic and linguistic modalities. Nonetheless, the original OT treats acoustic and linguistic feature sequences as two unordered sets in alignment and neglects temporal order information during OT coupling estimation. Consequently, a time-consuming pretraining stage is required to learn a good alignment between the acoustic and linguistic representations. In this paper, we propose a Temporal Order Preserved OT (TOT)-based Cross-modal Alignment and Knowledge Transfer (CAKT) (TOT-CAKT) for ASR. In the TOT-CAKT, local neighboring frames of acoustic sequences are smoothly mapped to neighboring regions of linguistic sequences, preserving their temporal order relationship in feature alignment and matching. With the TOT-CAKT model framework, we conduct Mandarin ASR experiments with a pretrained Chinese PLM for linguistic knowledge transfer. Our results demonstrate that the proposed TOT-CAKT significantly improves ASR performance compared to several state-of-the-art models employing linguistic knowledge transfer, and addresses the weaknesses of the original OT-based method in sequential feature alignment for ASR.