The Intel download site is... incorrect at best. They play a random game with the list of processors that are compatible with each Linux microcode release, and lately they can't even get the release date right...
Your processor is an i3-2348M, that's a Sandybridge processor with signature 0x206a7. The latest public version of the microcode for your processor is:
sig 0x000206a7, pf_mask 0x12, 2013-06-12, rev 0x0029, size 10240
Which is being distributed unmodified in all Intel Linux microcode releases since version 2013-08-08. So, the current Linux microcode releases are also compatible with your processor.
You are using Mint, which is based on Ubuntu, which is based on Debian. Debian's intel-microcode package has a changelog (unlike almost every other microcode distribution package), please look at /usr/share/doc/intel-microcode/changelog.gz:
(or visit that file using a browser capable of reading compressed files. Firefox works just fine).
You can use the "iucode-tool" package to know what is your processor signature. Install the iucode-tool package, and also the intel-microcode packages from Mint/Ubuntu/Debian and use the command:
It will tell you what is your processor signature.
If you want to know whether the Linux kernel applied the microcode update properly, look for "microcode updated early to revision"... log messages in the kernel log, examples:
journalctl -k -b | grep microcode
dmesg | grep microcode
grep microcode /var/log/kern.log
So, you can keep the current driver...