Galaxies with intense star formation often host multiphase, galaxy-scale winds powered by supernovae and fast stellar winds. These are strong enough to disrupt the star-forming interstellar medium, and they chemically enrich the surrounding circumgalactic medium. However, their launching mechanism remains unknown. Here we show that thermal gas pressure is sufficient to drive the multiphase wind in the prototypical starburst galaxy M82. Using a high energy-resolution ($ΔE = 4.5$ eV) XRISM Resolve spectrum, including detections of FeXXV 6.7 keV, ArXVII 3.1 keV, and SXVI 2.6 keV, we measure the temperature ($T = 2.3^{+0.5}_{-0.2} \times 10^7$ K) and mass ($M \approx 6 \pm 2 \times 10^5$ M$_\odot$) of the hot gas in the starburst and provide the first direct measurement of its line-of-sight velocity dispersion ($σ= 595^{+464}_{-128}$ km s$^{-1}$). These values are consistent with a freely-expanding wind exceeding the galactic escape velocity. The size of the FeXXV-emitting region suggests a hot gas outflow rate of $\dot{M} \approx 4$ M$_\odot$ yr$^{-1}$, carrying a total energy of $\dot{E} \approx 2 \times 10^{42}$ erg s$^{-1}$. This is sufficient to drive the molecular, atomic, and ionized outflows while transporting up to $\approx 2$ M$_\odot$ yr$^{-1}$ of hot gas to the intergalactic medium. The estimated supernova rate implies that $\approx$ 60% of the supernova energy must be thermalized in hot gas. Our results suggest that additional driving mechanisms, such as cosmic-ray pressure, are not required to launch the wind.