Laptop Battery comes with a 1yr Standard Limited Warranty when brand new because 1 year is the life expectancy of the battery. If you want a better battery, call Lenovo Laptop Battery's Support Hotline Toll Free # 1-800-426-7378, then tell the person who will take your call that you want to purchase a new battery for your computer but you want to know if they have a high performance 6cell or an 8 cell a 9cell battery available for your Edge 0578CTO model computer. The more cells the battery has, the longer it will last before you need to recharge it again.
FYI: I always tell my customers, a laptop's battery is similar to a cell phone's. You charge it when it's depleted & you unplug the adapter when it is already fully charge (this will prevent the battery from getting overcharged & extend the life of the HP Laptop Battery). So for less hassle, I always advice my customers to just remove the battery if they plan to use the computer for long hours straight (more than 1 hour) and just run it on AC power alone so as not to overcharge it & shorten the battery life.
FYI, laptop, as the name itself... well, I really don't use it on my lap b'coz sometimes our leg, the bed cover or some clothing may already be blocking the air vent without our knowledge.
Also, if your computer is running a lot of applications that means that the HDD (Hard Disc Drive) is moving very fast and any minute (small) movements of your legs creates vibrations inside (which we wont see from the outside) that causes damage to the HDD discs, and eventually in a long time (when the damage is too much and in some cases the HDD makes a sound) the hard drive will crash. So, if your laptop came with a HDD protection utility, just like what Toshiba and HP has, you can always lower down the sensitivity level to level 2 or 1 but never completely disable the protection utility to prevent the HDD from getting damage from the inside and use the computer on a stable surface. Now, like what I always tell my customers, to always create a restore point (every last day or first day of the month) and make sure that you constantly back-up any important pictures, documents or files from your HDD to a Flash Drive/Thumb Drive or writable DVD±R or an external HDD, so that you will not lose any of these info just in case something bad happens.
As you know, dust is almost always in the air. The air vents needs checking from time to time for accumulated dust might have clogged in the air passage way within the laptop itself. Use a flash light to check in the air vents. If you feel no air coming out, then have the fan changed b'coz it's not working anymore. Check the bottom of your computer, it usually has rubber pads that provides ample space between the laptop case bottom and the table. For the computers that I have used, these rubber pads provide enough clearance for ventilation for the hot air though it's not enough. It never hurts to be cautious, so for my own laptop, I bought a $15 2-fan Cooler Master U2 Cooling Pad from MicroCenter to help flush away the heated air from the bottom air vents of my laptop. Cool thing about the Cooler Master U2 is that you can position the fans on the right spot for better ventialation.