  Seagrasses are key structural elements in coastal ecosystems, and studying
how temperature affects these species is crucial to anticipate the implications
of global warming. In this work, we use an empirically-based numerical model to
study the combined dynamics of {\it Posidonia oceanica} and {\it Cymodocea
nodosa} and their resilience to sea warming. The model is parametrised using
seagrass growth rates measured at the Western Mediterranean Sea. Under
favorable growth conditions, our simulations predict the emergence of a
coexistence region at the front between mono-specific meadows. This region can
be characterised by its width and local shoot densities, which are found to
depend on the coupling parameter between {\it Posidonia oceanica} and {\it
Cymodocea nodosa} species. Such regions have been empirically observed in Ses
Olles de Son Saura (Balearic Islands, Western Mediterranean Sea). A comparison
between the field measurements at the study site with the model predictions has
been used to fit the value of the coupling parameter. Field data also relates
the width of the coexistence region to the average length of {\it Posidonia
oceanica} leaves at the front. Remarkably, a linear relationship is found
between the coupling parameter and the leaf length. In the presence of sea
warming, the model predicts an exponential decay in the population of {\it
Posidonia oceanica}, which is highly sensitive to temperature. This behaviour
is a direct consequence of the clonal nature of the plant and can be
characterised by the model parameters. Considering a scenario of high
greenhouse emissions, our model forecasts that {\it Posidonia oceanica} meadows
will lose 70$\%$ of their population by the year $2050$. {\it Cymodocea
nodosa}, with higher thermal resilience, acts as an opportunistic species
conquering the space left by the degraded {\it Posidonia oceanica}.
