No harm adding a heat mat to a bearded dragon's tank
to provide a secondary or even tertiary supplemental heat source and a warm place to nap / sleep , this is the kind of setup , BASED ON A 7W HEATPAD , I have in all my bluetongue skink and bearded dragon timber tanks and have in my 120L water skink tub , and had in my 100L rearing tubs , and have a 5W version that goes under my 10L RESCUE HOSPITAL TUB :
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all my skinks and dragons have loved their warmed hides (sitting ontop heated tiles).
Best that the heatpad be placed under something like a ceramic wall or floor tile to even out the heat and prevent burns if the heatpad overheats , I sandwhich mine to ensure the heatpad has no physical contact with timber or plastic (tub) or the reptile, the tile evens out the temperature and holds heat .
I recommend heatpads that have a temperature restriction to not higher than 38 degC.