Just to stave off any ungrounded worries, the heat mat didn't crack the cabinet. The amount of time and degree of heat that it would take to damage wood under and below 3/4 plywood isn't something that a heat mat could generate without severe damage to the mat and tank above (to say nothing of the snake).
Heat mats are commonly used directly attached to PVC (which starts to soften in water just off the boil -- 200F or so), under polypropylene tubs (melting point in the low 300sF), very safely.
FYI, the R value (insulating value) of plywood is slightly more than that of ceramic tile, and plywood can be had that's thicker than tiles. The R value of a 3/8" tile is 0.375, and that of 3/4" plywood is 0.93.
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