An e-LKPD based on guided inquiry has been developed using liveworksheets on the subject of heat and its transfer. The primary objective of this paper is to generate an inquiry-based e-LKPD that is demonstrably feasible, practical, and effective in enhancing students' critical thinking ability and mathematical representation. The methodology adopted for this development study adheres to the ADDIE model. The sampling procedure employed in the study utilized the cluster random sampling technique. Data acquisition was carried out using both testing and non-testing instruments. For the analysis of the gathered data, several techniques were applied: Aiken's V statistic was used for instrument validation, SBI was applied to the student response questionnaires, and the effectiveness analysis utilized MANOVA and GLM. This study’s main results are: (1) the inquiry-based e-LKPD utilizing Liveworksheet is suitable for deployment in advancing critical thinking and mathematical representation, as confirmed by assessments from expert validators, practitioners, and peers. (2) the developed e-LKPD is operationally practical for fostering these skills, evidenced by feedback collected through student response questionnaires concerning the learning medium. (3) the inquiry-based e-LKPD is demonstrably effective in enhancing students' critical thinking and mathematical representation, based on the improvement observed in students' pre-test and post-test scores following the use of the developed resource. A distinctive feature of this research lies in the seamless integration of the guided inquiry e-LKPD with the Liveworksheet. This integration allows students access to the learning material at any time, thereby contributing to the advancement of their critical thinking and mathematical representation ability.