We compare spanning-tree counts at a fixed number of vertices for Cartesian products of paths $P_r$, $r\ge1$, or cycles $C_s$, $s\ge3$. With the number $d$ of factors fixed, an equal-volume tuple that is more balanced in the logarithmic majorization order has at least as many spanning trees, with equality only for permutations. This comparison persists after adjoining any fixed finite connected Cartesian factor; equal-sided blocks therefore uniquely maximize the count at admissible block volume $n^d$. We prove the comparison through strict log-convexity of one-dimensional heat traces in logarithmic length. The Hartman--Watson representation expresses the cycle interpolation as a positive mixture of theta functions, and the path case follows from it. The same heat-trace order decreases every positive inverse-power sum of the nonzero Laplacian eigenvalues, and hence the total effective resistance. Cylinders behave differently: square balancing can fail. For $P_r\square C_s$ of area $N=rs$, extending the product formula to real height and optimizing over integer circumferences $3\le s\le N$ yields an optimum on the scale $N^{1/3}$. Along areas having a divisor asymptotic to that optimum, quantitative estimates place every graph-maximizing circumference on the same scale. For two-dimensional tori, balancing remains optimal, but the gain in the logarithmic spanning-tree count admits no positive uniform lower bound proportional to the decrease in the side sum.

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