Does the amp have a volt meter on it? That tends to be pretty helpful in determining if it has enough power. I had to run an 8 gauge wire from my battery to the amp to get enough current to power an audiobahn 6 channel 6601t, with a dual voice-coil audiobahn 12 inch eternal. In the summer mine hits a thermal protection unitl I roll down the windows and ventilate the car, but that does not sound like thermal to me. It could also be the wrong impedance for your amp/sub combo. If you are making these speakers distort, you should be deaf by now. a 1000 watt amp is no force to be reckoned with. Your sub is 1.5 to 4 ohms. I posted a link to where you can check if it is wired properly. If these are distorting, it sounds like you have these wired for the wrong impedance. There is no way you should be making this setup distort at all without blowing out windows. It could be that you need 2 batteries, or if you are a pro DIYer Get some A123 batteries from a dewalt product. They have insane discharge. But I would recommend just getting a new battery (see bottom link), and making sure you have a 4-8 gauge wire going to the amp. I know a lot about batteries, as I built my own EV, so tell me how you have these subs wired, and how you have the amp wired to the battery.
http://www.crutchfield.com/S-B5qDIPXbsfV/learn/learningcenter/car/subwoofers_wiring.html
http://akamaipix.crutchfield.com/ca/learningcenter/car/subwoofer_wiring/2DVC_4-ohm_mono.jpg
http://www.optimabatteries.com/audio_electronics/