We present results of a ^ { 12 } CO J = 3–2 survey of 125 nearby galaxies obtained with the 10-m Heinrich-Hertz-Telescope , with the aim to characterize the properties of warm and dense molecular gas in a large variety of environments . With an angular resolution of 22 ^ { \prime \prime } , ^ { 12 } CO 3–2 emission was detected in 114 targets . Based on 61 galaxies observed with equal beam sizes the ^ { 12 } CO 3–2/1–0 integrated line intensity ratio R _ { 31 } is found to vary from 0.2 to 1.9 , with an average value of 0.81 . No correlations are found for R _ { 31 } to Hubble type and far infrared luminosity . Possible indications for a correlation with inclination angle and the 60 \mu m/100 \mu m color temperature of the dust are not significant . Higher R _ { 31 } ratios than in “ normal ” galaxies , hinting at enhanced molecular excitation , may be found in galaxies hosting active galactic nuclei . Even higher average values are determined for galaxies with bars or starbursts , the latter being identified by the ratio of infrared luminosity versus isophotal area , log [ ( L _ { FIR } / L _ { \odot } ) / ( D _ { 25 } ^ { 2 } /kpc ^ { 2 } ) ] > 7.25 . ( U ) LIRGs are found to have the highest averaged R _ { 31 } value . This may be a consequence of particularly vigorous star formation activity , triggered by galaxy interaction and merger events . The nuclear CO luminosities are slightly sublinearly correlated with the global FIR luminosity in both the ^ { 12 } CO J = 3–2 and the 1–0 lines . The slope of the log-log plots rises with compactness of the respective galaxy subsample , indicating a higher average density and a larger fraction of thermalized gas in distant luminous galaxies . While linear or sublinear correlations for the ^ { 12 } CO J = 3–2 line can be explained , if the bulk of the observed J = 3–2 emission originates from molecular gas with densities below the critical one , the case of the ^ { 12 } CO J = 1–0 line with its small critical density remains a puzzle .