RowHammer is a circuit-level DRAM vulnerability where repeatedly accessing (i.e., hammering) a DRAM row can cause bit flips in physically nearby rows. The RowHammer vulnerability worsens as DRAM cell size and cell-to-cell spacing shrink. Recent studies demonstrate that modern DRAM chips, including chips previously marketed as RowHammer-safe, are even more vulnerable to RowHammer than older chips such that the required hammer count to cause a bit flip has reduced by more than 10X in the last decade. Therefore, it is essential to develop a better understanding and in-depth insights into the RowHammer vulnerability of modern DRAM chips to more effectively secure current and future systems. Our goal in this paper is to provide insights into fundamental properties of the RowHammer vulnerability that are not yet rigorously studied by prior works, but can potentially be $i$) exploited to develop more effective RowHammer attacks or $ii$) leveraged to design more effective and efficient defense mechanisms. To this end, we present an experimental characterization using 248~DDR4 and 24~DDR3 modern DRAM chips from four major DRAM manufacturers demonstrating how the RowHammer effects vary with three fundamental properties: 1)~DRAM chip temperature, 2)~aggressor row active time, and 3)~victim DRAM cell's physical location. Among our 16 new observations, we highlight that a RowHammer bit flip 1)~is very likely to occur in a bounded range, specific to each DRAM cell (e.g., 5.4% of the vulnerable DRAM cells exhibit errors in the range 70C to 90C), 2)~is more likely to occur if the aggressor row is active for longer time (e.g., RowHammer vulnerability increases by 36% if we keep a DRAM row active for 15 column accesses), and 3)~is more likely to occur in certain physical regions of the DRAM module under attack (e.g., 5% of the rows are 2x more vulnerable than the remaining 95% of the rows).