First of all, you have a 1st (not 3rd) generation Intel Core i5 processor. It is installed onto a 5 Series board.
I have no idea what you are trying to imply regarding a "lack of thermal monitoring technologies". While there are improved technologies in later generation processors, your processor has all of the technologies necessary for managing processor temperatures. What do you feel is lacking (other than support from either Intel or Microsoft)?
Not implying anything just need to know under what circumstances my 1st gen CPU might get into trouble that 3rd gen can handle. Does installed BIOS that later got updated by maintenance play the role in that too.
From a thermal monitoring standpoint, the 3rd generation processor really offers nothing extra. That said, the age of a system supporting a 1st generation processor is going to be more problematic than that of a system supporting a 3rd generation processor. The biggest differences are going to be with the capabilities and sophistication of the BIOS provided.
As I look at things, the biggest area of concern between a system with 1st generation processor and a system with 3rd generation processor is going to be in the support offered by Intel and Microsoft. Intel and Microsoft are not supporting Windows 10 on platforms with 1st generation processors. I am not saying that Windows 10 will not work on these systems; I am saying that no support is being offered for the processor or the chipset on the motherboard if problems do occur and no effort is being put into ensuring that device drivers will optimally (if at all) support this older hardware - and certainly, if a problem develops, no support for addressing this problem will be forthcoming. Now, for the system with 3rd generation processor, there are still concerns. While it is true that, for the most part, support is still being offered by Intel and Microsoft, there are certain areas where support *has* already been dropped (Intel RST, for example). More concerning is the fact that we are within a year of support for 3rd generation processors and supporting chipsets being dropped completely.
Bottom line, I recommend that you make the move to even-newer hardware that both of these generations sooner rather than later.
So from temperature monitoring and safety measure standpoint I need not worry. But since Windows 10 OS(not using it currently but if I do) drivers are not compatible with handling hardware under exceptions, which BIOS would be recommended if not the American Megatrends one currently installed to ensure as a last safety measure does it even make any difference to change to another one.
Long gone are the days where you can simply replace the BIOS on a PC. There are simply too many hurdles WRT hardware initialization, security, etc. that would need to be overcome. I really don't see this helping you anyway.
Face it, you are running an 8 year old processor. It is already past the average (6 year) MTBF for many the components used on the supporting motherboard. Things are going to start going wrong soon (if they haven't already). Avoid the aggravation; it is time to upgrade - and going up to that 3rd generation processor isn't enough, IMHO.