A clear theoretical understanding of the protein folding problem both in kinetic as well as in thermodynamic aspects, has not yet been achieved. In this context, we have studied here the possible role of solvent on the equilibrium collapse transition characteristics of a polymer that serves as a simple model protein chain. We have assumed the standard bead-stick representation of the polymer where each bead possesess physical properties similar to that of the amino acids of the real proteins. The equilibrium transition was studied by Metropolis Monte Carlo simulation of the chain on a simple cubic lattice. We have presented tentative arguments in favor of considering the stability factor of a nearest neighbor bead-bead pair to be temperature dependent, on the basis of a change of the order of water molecules in the immediate vicinity of the protein molecule. We have considered two different stability schemes; (i) temperature dependent and (ii) temperature independent and have shown that only in the case of temperature dependent stability scheme, there may be a cooperative collapse transition in the case of a model chain which is very similar to that observed in real experiments, while, in the other case, there is practically no cooperative transition over the same temperature range. The transition has been described by the evolution of two different physical quantities (i) the average number of bead contacts ((N) over bar(c)) and (ii) the average rms radius ((R) over bar(rms)). In both the cases cooperative transitions have been observed for the temperature dependent stability factor. The results show that the cooperativity in such transitions might be, at least partially, a consequence of the temperature dependent property change of the aqueous solvent. We have also studied the chemical denaturant induced transition of model chain in a similar framework. The results presented here are mainly on homopolymers.