My sub is getting distorted at high volumes please help?

Hi i have a JL 13w7 powered by a JL 1000/1 amp and a 1 farad rockford fosgate 1 farad cap. My sub works perfectly fine when i have the volume low or medium but when i increase to to a higher level it begins to distort. When i took it to the guys that installed it they told me that the coils are overheating but i feel they just want me to buy a sub from them as they insisted that JL audio suck and that the fosgate t2's they have are better. Also, i have it in a sealed box that's built to spec. I feel that it might just be tuned wrong but at the same time i don't know much about car audio.