We have carried out submillimeter (CO)-C-12(J = 3-2) observations of six giant molecular clouds (GMCs) in the Large Magellanic Cloud (LMC) with the ASTE 10 m submillimeter telescope at a spatial resolution of 5 pc and very high sensitivity. We have identified 32 molecular clumps in the GMCs and revealed significant details of the warm and dense molecular gas with n(H-2) similar to 10(3)-10(5) cm(-3) and T-kin similar to 60 K. These data are combined with (CO)-C-12(J = 1-0) and (CO)-C-13(J = 1-0) results and compared with LVG calculations. The results indicate that clumps that we detected are distributed continuously from cool (similar to 10-30 K) to warm (greater than or similar to 30-200 K), and warm clumps are distributed from less dense (similar to 10(3) cm(-3)) to dense (similar to 10(3.5)-10(5) cm(-3)). We found that the ratio of (CO)-C-12(J = 3-2) to (CO)-C-12(J = 1-0) emission is sensitive to and is well correlated with the local H alpha flux. We infer that differences of clump properties represent an evolutionary sequence of GMCs in terms of density increase leading to star formation. Type I and II GMCs (starless GMCs and GMCs with H II regions only, respectively) are at the young phase of star formation where density does not yet become high enough to show active star formation, and Type III GMCs (GMCs with H II regions and young star clusters) represent the later phase where the average density is increased and the GMCs are forming massive stars. The high kinetic temperature correlated with H alpha flux suggests that FUV heating is dominant in the molecular gas of the LMC.