We report ALMA Cycle 3 observations in CO isotopes toward a dense core, MC27/L1521F in Taurus, which is considered to be at an early stage of multiple star formation in a turbulent environment. Although most of the high-density parts of this core are considered to be as cold as $sim$10 K, high-angular resolution ($sim$20 au) observations in $^{12}$CO ($J$ = 3--2) revealed complex warm ($>$15--60 K) filamentary/clumpy structures with the sizes from a few tens of au to $sim$1,000 au. The interferometric observations of $^{13}$CO and C$^{18}$O show that the densest part with arc-like morphologies associated with the previously identified protostar and condensations are slightly redshifted from the systemic velocity of the core. We suggest that the warm CO clouds may be consequences of shock heating induced by interactions among the different density/velocity components that originated from the turbulent motions in the core. However, such a small-scale and fast turbulent motion does not correspond to a simple extension of the line-width-size relation (i.e., Larson{}s law), and thus the actual origin remains to be studied. The high-angular resolution CO observations are expected to be essential in detecting small-scale turbulent motions in dense cores and to investigate protostar formation therein.