Interstellar absorption lines up to J″= 10 in the (2, 0) band and up to J″= 6 in the (3, 0) band of the C2 A1Πu-X1Σ+g system are detected toward star Cernis 52 (BD +31°640) in the Perseus molecular complex. The star lies in a reddened line of sight where various experiments have detected anomalous microwave emission spatially correlated with dust thermal emission. The inferred total C2 column density of N(C2) = (10.5 ± 0.2) × 1013 cm-2 is well correlated with that of CH, as expected from theoretical models, and is among the highest reported for translucent clouds with similar extinction. The observed rotational C2 lines constrain the gas kinetic temperature T and the density n=n(H) +n(H2) of the intervening cloud to T= 40 ± 10 K and n= 250 ± 50 cm-3, respectively. This is the first determination of the gas kinetic temperature and particle density of a cloud with known anomalous microwave emission.