You should have to worry about the box melting. Heat pads will get no where near the melting point of plastic, but you should still use something to control the temperature.
I'd consider picking up some heat tape and a thermostat and installing them in some sort of shelving system or in fish tanks. I would be hesitant to heat plastic bins without a thermostat-controlled heat source. Even a cheap thermostat is better than going without. Simply using a heat lamp or uncontrolled heating pad would open the door to improper temps, cooked geckos or at worst a fire that could take down your entire house. I also like my racks because the small gap at the top of each bin allows for a it of extra airflow without allowing the babies to escape. Plastic lids on the bins would probably need a few more holes drilled in them for proper airflow.