The high-throughput data generated by new biotechnologies used in biological studies require specific and adapted statistical treatments. In this work, we propose a novel and powerful framework to manage and analyse multi-omics heterogeneous data to carry out an integrative analysis. We illustrate it using the package mixOmics for the R software as it specifically addresses data integration issues. Our work also aims at confronting the most recent functionalities of mixOmics to real data sets because, even if multi-block integrative methodologies exist, they still have to be used to enlarge our know-how and to provide an operational framework to biologists. Natural populations of the model plant Arabidopsis thaliana are employed in this work but the framework proposed is not limited to this plant and can be deployed whatever the organisms of interest and the biological question. Four omics data sets (phenomics, metabolomics, cell wall proteomics and transcriptomics) have been collected, analysed and integrated in order to study the cell wall plasticity of plants exposed to sub-optimal temperature growth conditions. The methodologies presented start from basic univariate statistics and lead to multi-block integration analysis, and we highlight the fact that each method is associated to one biological issue. Using this powerful framework led us to novel biological conclusions that could not have been reached using standard statistical approaches.