We report discovery of two CO clouds which are likely falling down to the Galactic plane at more than $35$ km s$^{-1}$. The clouds show head-tail distributions elongated perpendicular to the Galactic plane at $l=331.6^{\circ}$ and $b=0^{\circ}$ as revealed by an analysis of the Mopra CO $J=$1-0 survey data. We derived the distance of the clouds to be $2.46 \pm 0.18$ kpc based on the Gaia Data Release 3. The CO clouds have molecular masses of $4.8\times 10^3\ M_{\odot}$ and $3.5\times 10^3\ M_{\odot}$, respectively, and show kinetic temperature of 30-50 K as derived from the line intensities of the $^{13}$CO $J$=2-1, $^{12}$CO $J$=1-0, and $^{13}$CO $J$=1-0 emission. The temperature in the heads of the clouds is significantly higher than 10 K of the typical molecular clouds, although no radiative heat source is found inside or close to the clouds. Based on the results, we interpret that the present clouds are falling onto the Milky Way disk and are significantly heated up by the strong shock interaction with the disk HI gas. We suggest that the clouds represent part of the HI intermediate velocity clouds falling to the Galactic plane which were converted into molecular clouds by shock compression. This is the first case of falling CO clouds having direct observed signatures of the falling motion including clear directivity and shock heating. Possible implications of the CO clouds in the evolution of the Galactic interstellar medium are discussed.