HTC One is the first phone I've seen with a LiPoly battery so I'm positing this here, if any mod thinks there would be a better place to post this, go ahead and move it. Here are a few things about LiPolys you should know. Two of the reasons they had previously not been used in cell phones was because they were costly, and are downright deadly without the right precautions and failsafes in place. First, A lipoly will be damaged and no be rechargeable if the charge goes below a set voltage, for a single cell 7.2V that is around 6V. The charge rate of a Lipoly should be 4.2V, if there are two or more cells in a pack, these MUST be balanced on a regular basis to prevent the battery from exploding. do NOT charge at more than 1C (one times capacity of the battery) or the pack could explode. Do NOT puncture the cell EVER, it could explode or start a fire. The fumes are toxic and can kill you. NEVER short out the battery it could explode or catch fire. large impacts can also cause internal shorting. Lipolys work better when they are warm, but reaching temperatures in excess of 160 degrees F can damage them, anything over that can easily cause the pack to swell which can lead to fire or explosion. Lipoly's do not self discharge.
What does all this mean to you? Nothing so long as HTC has incorporated proper circuitry to keep the battery from getting too hot, from over charging, from charging too fast or too slow, and monitor the battery health. A few things you can do to keep your batter lasting longer is let the phone cool after a long hard gaming session where the phone may get hot, try not to drop or throw the phone, don't run over it with your car, if it suffers a severe impact, it may be a good idea to turn it off, place it in a pyrex bowl with a layer of sand on the bottom, and let it sit for a few hours just in case (probably overkill but hey, better safe than sorry). HTC did design this phone fairly well. Making the battery un-removeable lessons the chance of the end user (you and I) shorting it out inadvertently. They sandwiched it between a circuit board and the digitizer, if you drop the phone, the back may bend, and anything pressed against the back could suffer more impact damage than where it is currently positioned. Also, not only do Lipolys have a longer lifespan than LiIon, they are also more efficient and weigh less. As a sealed battery, they were a good choice!
Let me again reiterate, do not worry about your phone getting too hot! HTC and any other manufacturer using Lipolys know the inherent dangers of mishandling and would have designed their phone around this. I suspect your phone would shut down to save the hardware (processor, battery, etc.) before it got too hot to do any damage both long and short term. Do let the phone cool before charging it if you can as it will help prolong the life of your battery. Don't worry about the battery having "memory" it doesn't, so you can start charging it an any percentage without decreasing the lifespan of the battery. Do not leave your phone on the dashboard of your car, especially if it's the black version, excess heat can cause damage to it, if you are on a road trip in the summer and you have AC on or sufficient air flow in the car, I wouldn't worry, as I said, it will likely shut down if it gets too hot, if it does shut down, put it someplace out of direct sunlight, and preferably out of extreme heat. Use common sense and your battery should outlast the phone! Enjoy!