In this work, we explore a kind of geometrical effect in the thermodynamics of artificial spin ices (ASI). In general, such artificial materials are athermal. Here, We demonstrate that geometrically driven dynamics in ASI can open up the panorama of exploring distinct ground states and thermally magnetic monopole excitations. It is shown that a particular ASI lattice will provide a richer thermodynamics with nanomagnet spins experiencing less restriction to flip precisely in a kind of rhombic lattice. This can be observed by analysis of only three types of rectangular artificial spin ices (RASI). Denoting the horizontal and vertical lattice spacings by [Formula: see text] and [Formula: see text], respectively, then, a RASI material can be described by its aspect ratio [Formula: see text]. The rhombic lattice emerges when [Formula: see text]. So, by comparing the impact of thermal effects on the spin flips in these three appropriate different RASI arrays, it is possible to find a system very close to the ice regime.