It's the "and aquariums" part that concerns me. It's usually only the reptile-specialty bulbs that throw enough UVB. Bulbs made for fish don't need to throw so much UVB and the mercury needed to generate UV is expensive so it's seldom added to bulbs not specifically made for basking species.
Heat tape isn't very useful for beardies, they are heliotherms that absorb infrared and ultraviolet radiation into their bony armor plating to thermoregulate properly. Ambient heat from mats, tape or ceramic heat emitters doesn't penetrate into their bones so they can store up that heat. You are better off with a good quality basking/UVB lighting setup without heat tape.
It depend on the beardie himself as to whether 35 C is too hot or not hot enough. Juveniles often enjoy basking temps as high as 45 but adults often prefer it around 30. Try it and see, if s/he is gaping and moving away gradually lower the basking temp a few degrees at a time until you find your own dragon's comfort zone.
Beardies need a core body temperature of 103 degrees F in order to properly digest their food, I believe that is somewhere around 39 to 40 degrees C, so I'd start with temps at least that high if the dragon is less than around 200 grams. By the time they reach that size, if they are exposed to enough infrared and ultraviolet radiation they can get a high enoug core body temperature at lower cage temps, but little ones just don't have enough bone mass and body fat to achieve that kind of heat without it coming directly from their environment.
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