It sounds like "as new" is dishonest or there is malware on the system. The first thing to do would be to check the fully charged capacity /health of the battery - if its less then about 95% of new capacity I dont think it can be considered "as new" (and I've returned a laptop on that basis). If its < 80% the battery is considered end of life.
You did not advise your OS, but if its Windows 10 you can generate a report by running the following command in a cmd box launched as administrator, then use a web browser to read the resulting report:
powercfg /batteryreport /output "C:\path\to\batteryinfo.html
Another thing to check is self discharge - if you fully charge the laptop then turn it off overnight how much charge does it lose? If a cell is damaged, it could explain heat buildup and short runtime.
The second thing to look at is the CPU utilization. It sounds like there might be something eating up all the available CPU - this will drain the battery fast and cause a lot of heat which will cause the fan to be on. Look at task manager to see cpu utiluzation and processes and run av and anti-malware across the system.
Also, look at power profiles. The system will perform more responsively but drain a lot more resources if the power profile is set to performance as opposed to a more balanced mode.
Lastly, try look into the fan grate and see if there is lint blocking the airflow.
Thank you for your answer. I tried to run F12 diagnostic and everything is ok. The problem is the fan starts spinning fast and stops from time to time when no program is running – Mehdi IT – 2019-09-02T11:40:09.600
You must understand it is not when no program is running, it is when no program you SEE is running. Your computer is always running programs. An Operating System is just a big collection of programs. You have not described any hardware faults, and the F12 tests are just for hardware diagnostics and will not tell you about any software problems. – music2myear – 2019-09-02T22:02:26.913
How can I check if there is any software than is making my fan spinning fast ? – Mehdi IT – 2019-09-03T08:45:31.643
Start by using the correct and more accurate terms. No software is directly making your fans spin fast. There isn't a measurement of "how fast will this program make my fans spin" except for tools that monitor fan speed. You are looking for processes that are using a large amount of system resources. On Windows you find this in the Task Manager, to start with. – music2myear – 2019-09-04T03:02:18.863