Where I live, the warranty is 2 years.
About Kaspersky, maybe it installed in one of those installers that include extra software and I failed to deselect it for install. Whatever is on my computer, it is not registered in the installed programs.
For temperatures, I've been using speedfan. It monitors all temperature sensors, not only the CPU one.
I know it is not overheating. This even happens when it is cool; CPU temperature below 50ºC. At a time when I can place my hand on the exit of the fan output and keep the hand there (for a while until it becomes too hot). Also, at normal use, the fan is never at full speed. With the fan working, overheating only happens after the fan runs at maximum speed.
I do loads of precautions to prevent dust from entering the computer. I can execute a 100% CPU usage program, the fan speeds up but nothing wrong happens to the computer. On the other hand, while almost at idle, it can freeze.
Some minutes ago, I was playing a full screen game that is CPU intensive. Max temperature of any core was 63ºC with a room temperature of 38ºC (yes, it is hot here). Not it is 35ºC here and the CPU is ~32% usage. Temperatures are of 49-52ºC which seems normal to me.
That's how I think it is not overheating.
Also:
"and the CPU heating up as fast as it can."
This is when the computer freezes, not before. I just thought it could be useful information. For me, it seems like it is related to an infinite loop somewhere but I'm not sure.