I've been using Linux Mint 15 on my Thinkpad Carbon X1 since about when it came out. It's been running pretty well, but I finally got to the point where I'm doing more ./configure than I am apt-get install as the repository is so outdated.
Linux Mint 17 XFCE recently came out, and is a “Long Term Release” (a concept I believe Mint is borrowing from Ubuntu). This means the repository should be more up to date for about five years, instead of Mint 15's 2-ish years.
At any rate, here is the procedure to follow to get Linux Mint 17 (or Debian or Ubuntu really) using the most recent Kernel (as of this writing it is 3.15.3). The stock Kernel in Mint 17 is 3.13.0. The Kernel in my existing Mint 15 is 3.8.0.
First, download the appropriate packages. I'm assuming you're using a 64-bit machine (and have been for the last 4 years) so the instructions are for that. To adapt for 32-bit, manually browser around the download URLs until you find the sibling half-bitted package.
mkdir -p ~/Downloads/kernel && cd ~/Downloads/kernel wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v3.15.3-utopic/linux-headers-3.15.3-031503-generic_3.15.3-031503.201407010040_amd64.deb wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v3.15.3-utopic/linux-headers-3.15.3-031503_3.15.3-031503.201407010040_all.deb wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v3.15.3-utopic/linux-image-3.15.3-031503-generic_3.15.3-031503.201407010040_amd64.deb sudo dpkg -i *.deb
And poof, you've got the latest kernel.
You may be wondering; why do I want to upgrade my kernel at all? Surely if Mint recommends an older kernel, there must be a reason to use it? And you're probably right. With each new kernel update there comes new stability and security updates. There also comes new problems and potential version mismatches. Upgrade at your own risk.
I'm writing this post from within Mint 15. I've done these upgrades in a VM. I'll update this post once my Thinkpad has been updated with any issues I find.