We have studied the time-scale and temperature dependence of the magnetization reversal in perpendicular magnetic recording media. One of the under-reported phenomena associated with this reversal is the thermal dependence of the squareness of the magnetic hysteresis loop. Understanding this phenomenon is important because the coercive squareness parameter S* is often used to evaluate the strength of the magnetic exchange-coupling interactions between the grains. In this work, we demonstrate that S* is a dynamic quantity which depends on the thermal agitation of the magnetization, and it is imperative to take this dependence into account in interpreting magnetic and microstructural effects. Based on the Sharrock model for the dynamic coercivity, we built an expression for the time-scale and temperature dependence of S* in highly oriented perpendicular magnetic recording media. Fits of experimental data to the resulting expression were then used to extract the intrinsic squareness parameter Sint* which originates in the thermal-independent demagnetization and exchange-interaction effects. Sint* was estimated for two sets of perpendicular recording media samples. For the first set of media samples showing progressively smaller grain sizes, the values of S* measured at the normal magnetometry time-scales of milliseconds to seconds indicated progressively smaller values. In contrast, the values of the thermal-independent Sint* determined from applying the above model were progressively larger. This discrepancy can only be explained on the basis of progressively stronger intergranular exchange coupling, which is offset by strong thermal effects at small grain sizes. For the second set of - - media samples with increasingly larger segregant oxide content, progressively smaller values of both S* and thermal-independent Sint* were observed, thus verifying the strong intergranular segregation effects due to greater nonmagnetic grain boundary phase. The phenomenological model for thermal-independent Sint* will be helpful in interpreting the microstructural and magnetic properties of perpendicular magnetic recording media, especially as thermal effects become important in the approach to areal densities of 1 Tbits/in2.