I own the aforementioned Toshiba for a year and a half now without major issues.
The OS is Windows10 x64 Home Edition (I have it upgraded for almost 8 months of smooth operations).

Just a couple of weeks ago, I started facing SEVERE problems with my Laptop that ended in sudden shut offs.
Especially when engaged in several games and apps (which I otherwise have been using since the acquisition of the laptop without issues) , the laptop started increasing FAN SPEED beyond ordinary without it being able to keep a stable and viable performance/temperature. After a very brief duration in those games and apps, the laptop shuts off without a warning. When I restart it by pressing the ON Button, it proceeds into normally starting Windows again without any notification of why the previous sudden shut off happened (I would expect a faulty message or so).

Additional Info:
I have recently performed a factory reset (about 2.5 months ago), drastically reducing background apps that required increased resources, thus making the overall laptop performance smoother
After the factory reset I also installed via the Toshiba site the Toshiba Battery Utility, as well as the newest GPU drivers (Raden M270) via the respective utility. As a note here, I was constantly updating my GPU drivers without an issue for the past year or so as well.
I am also pretty positive in terms of 0 malware/Trojans/viruses that could affect overall performance since I have performed the factory reset and owning already for 15 months the Total McAffee Livesafe subscription, which I thoroughly use,

After the first couple of times that the sudden-shut off occurred (about a week ago), I opened the laptop to see whether my FAN was dirty and I blew away any small dust particles trapped there - There were VERY FEW, almost none, thus my fan was clean.
I am using an elevated laptop base that ensured proper airflow - no additional fans - (for the same duration almost 1.5 year now without issues).

I am desperate.
What can I do to determine whether it is indeed a FAN issue or something else? Could it be the cooling metallic piece that connects the CPU to the Cooler Fan (I am feeling that the laptop heats towards its middle as well, not only at the cooler fan output). Could it be increased CPU load by something else that is producing heat levels now that cannot anymore be handled by this FAN?

Should I go directly to the Toshiba representative for a FAN Replacement? here in Greece, the only Toshiba repair representative/collaborator has VERY BAD REVIEWS in terms of laptop handling and I am afraid to go so as to avoid further damage/mistreatment.

The laptop can only perform basic operations like browsing and some MS Office Apps. Other than that it shuts off.

My guarantee is about to expire in very few months and I would like to know whether I should ask for a fan replacement or perform some corrective actions myself. I would strongly prefer the latter.

Thank you in advance,
I could really use some good advice cause I am borderline desperate, since this laptop is not only leisure but also work focused (Matlab,, R , Data Analytics).