In this paper, we develop a new coarse-grained model, under the MARTINI framework, for Pluronic block copolymers that is able to describe the self-assembly mechanism and reproduce experimental micelle sizes and shapes. Previous MARTINI-type Pluronic models were unable to produce realistic micelles in aqueous solution, and thus our model represents a marked improvement over existing approaches. We then applied this model to understand the effects of polymer structure on the could point temperature measured experimentally for a series of Pluronics, including both normal and reverse copolymers. It was observed that high PPG content leads to dominant hydrophobic interactions and a lower cloud point temperature, while high hydrophilic PEG content shields the micelles against aggregation and hence leads to a higher cloud point temperature. As the concentration increases, the effect of polymer architecture (normal vs reverse) starts to dominate, with reverse Pluronics showing a lower cloud point temperature. This was shown to be due to the increased formation of cross-links between neighboring micelles in these systems, which promote micelle aggregation. Our results shed new light on these fascinating systems and opens the door to increased control of their thermal responsive behavior.