Question Changing hard disk firmware ?

i have blue screen when i boot hard drive from bios,and recently i contact seagate for that drive they said that my warranty expired
my hdd st1000dm010
What blue screen?
Can you show a screenshot?
(upload to imgur.com and post link)

Blue screens are not usually related to HDD firmware.
Where did you get the idea about changing firmware?

You should boot into windows and check drive health.
Use HDtune health. Post screenshot.

But your Seagate model has rather high failure rates.
Smartest thing would be just upgrading to SSD.
 
Check the Seagate web site for exact model number of your hard disk and whether or not there are any known issues with some firmware releases that have been fixed by an update.

If you believe your drive is exhibiting the issues described on the web site and you're prepared to risk "bricking" it, backup all the data, download the firmware update, disconnect all other hard disks and apply the update.

I'm assumimg you've run a thorough surface scan of the hard drive and found no bad blocks, pending sectors, etc.