A theoretical investigation of the denaturation characteristics of a supercoiled DNA has been presented employing a Metropolis Monte Carlo algorithm to examine the overall melting profiles of a supercoiled plasmid as the temperature is varied. We show that in contrast to a previously presented algorithm, this much simpler method is sufficient to explain almost all the overall denaturation characteristics and it also correctly calculates the detailed denaturation probabilities of each base pair at various degrees of supercoiling. We also present for the first time a theoretical investigation of the alkaline denaturation of a supercoiled plasmid. Although one can qualitatively reproduce the denaturation profiles using the present Monte Carlo algorithm, the agreement with experiment is not as good as in the case of thermal denaturation. The possible sources of discrepancy between theory and experiment have been discussed.