Your new battery isn't probably delivering maximum performance because it is uncharged. A new battery pack comes uncharged and it accepts only about 80% of its maximum charge capacity when its first charged. New batteries also require additional time on the first charge. You might need to let your new battery have several charge and discharge cycles so it can be up to full charge capacity and delivering maximum performance.
1. You used the device for a long period of time and the battery really got hot, just turn it off and use it again after 20-30 min. 2. Your fan that cools the device might be broken. The fan is what cools the device and stops it from overheating. If broken just remove the fan and add a new one in.