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We predict the 21-cm global signal and power spectra during the Epoch of Reionisation using the MERAXES semi-analytic galaxy formation and reionisation model, updated to include X-ray heating and thermal evolution of the intergalactic medium. Studying the formation and evolution of galaxies together with the reionisation of cosmic hydrogen using semi-analytic models (such as MERAXES) requires N-body simulations within large volumes and high mass resolutions. For this, we use a simulation of side-length $210~h^{-1}$ Mpc with $4320^3$ particles resolving dark matter haloes to masses of $5\times10^8~h^{-1}~M_\odot$. To reach the mass resolution of atomically cooled galaxies, thought to be the dominant population contributing to reionisation, at $z=20$ of $\sim 2\times10^7~h^{-1}~M_\odot$, we augment this simulation using the DARKFOREST Monte-Carlo merger tree algorithm (achieving an effective particle count of $\sim10^{12}$). Using this augmented simulation we explore the impact of mass resolution on the predicted reionisation history as well as the impact of X-ray heating on the 21-cm global signal and the 21-cm power spectra. We also explore the cosmic variance of 21-cm statistics within $70^{3}$ $h^{-3}$ Mpc$^3$ sub-volumes. We find that the midpoint of reionisation varies by $Δz\sim0.8$ and that the cosmic variance on the power spectrum is underestimated by a factor of $2-4$ at $k\sim 0.1-0.4$ Mpc$^{-1}$ due to the non-Gaussian nature of the 21-cm signal. To our knowledge, this work represents the first model of both reionisation and galaxy formation which resolves low-mass atomically cooled galaxies while simultaneously sampling sufficiently large scales necessary for exploring the effects of X-rays in the early Universe.