When a laptop is used for long periods of time, the battery becomes worn out and causes extreme heating when constantly charged. To alleviate this issue, try using the laptop without the charger plugged in. If heat is still produced, remove the battery and run the laptop on AC power. Lastly, if all else fails, you might have to buy a replacement battery, which you can order right from the Dell website:
http://accessories.us.dell.com/sna/productdetail.aspx?c=us&l=en&s=bsd&cs=04&sku=312-1387&mfgpid=229431
Hope that helps!