An attempt is made here to revisit structure formation in a proto-stellar cloud during the early phase of evolution. A molecular cloud subject to a set of various initial conditions in terms of initial temperature and amplitude of azimuthal density perturbation is investigated numerically. Special emphasis is on the analysis of ring- and spiral-type instabilities that have shown dependence on certain initial conditions chosen for a rotating solar mass cloud of molecular hydrogen. Generally, a star-forming hydrogen gas is considered to be initially at 10 K. We have found that a possible oscillation around this typical value can affect the fate of a collapsing cloud in terms of its evolving structural properties leading to proto-star formation. We explored the initial temperature range of the cloud between 8 K to 12 K and compared the physical properties of each within the first phase of proto-star formation. We suggest that the spiral structures are more likely to form in strongly perturbed molecular cores that initiate their phase of collapse from temperatures below 10 K, whereas cores with initial temperatures above 10 K develop, instead of a spiral structure, a ring-type structure which subsequently experiences fragmentation. A transition from a spiral to ring instability can be observed at a typical initial temperature of 10 K.