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Yes white styrofoam is fine, the kind of sheets you often see packaging or stryofoam coolers. You can get styrofoam sheets at hardware stores like Lowes or Home Depot.
By 'flush against the bottom' I mean having it press flat against the bottom of the tub, so the styrofoam will fill the gap and press the heat pad against the tub with more direct contact and insulate it. I'd just make sure to either cut a channel or leave a gap where the thermostat probe heat is so it doesn't get squished under the pressure. Does that make sense?
You can cover the entire bottom with stryofoam without needing to leave space. Stryofoam melting point temperature is 460F degress so I doubt it will melt. However if you really are worried, you could always use styrofoam only where the heatpad is and use furnitaure padding or risers to level the rest of the tub. Whatever keeps your mind at ease.
Speaking of thermostats which one are you using? If you really are scared one day yours will break down I would highly reccomend looking into Herpstats by Spyder Robotics! They are more expensive but are worth every penny, super accurate, loads of security features and a very long life span! (10 years +) They recently came out with more affordable models too. Seriously best purchase I've ever made and I know I can always rely on it.