cpu - PC is shutting down due to overheating but heat sink is cool to the touch

my PC is freezing up and shutting down. I have tried reseating the heatsink but the issue isn't fixed. I am very new to hardware maintenance and I'm not sure what to try next, any advice appreciated and thank you in advance.

Specs:

1. Machine: Mobo: ASUSTeK model: P8Z77-V LK v: Rev X.0x
   Bios: American Megatrends v: 0908 date: 11/16/2012


2. CPU: Quad core Intel Core i5-3570K (-MCP-) cache: 6144 KB
   flags: (lm nx sse sse2 sse3 sse4_1 sse4_2 ssse3 vmx) bmips: 27280
   clock speeds: max: 3800 MHz 1: 1600 MHz 2: 1600 MHz 3: 1599 MHz
   4: 1600 MHz


3. Graphics: Card: Intel Xeon E3-1200 v2/3rd Gen Core processor
   Graphics Controller
   bus-ID: 00:02.0
   Display Server: X.Org 1.18.4 drivers: intel (unloaded: fbdev,vesa)
   
   Resolution: 1440x900@59.89hz
   GLX RSystem Temperatures: cpu: 87.0C mobo: 27.8C
   Fan Speeds (in rpm): cpu: 0enderer: Mesa DRI Intel Ivybridge Desktop
   GLX Version: 3.0 Mesa 11.2.0 Direct Rendering: Yes


4. Audio: Card Intel 7 Series/C210 Series Family High Definition
   Audio Controller
   driver: snd_hda_intel bus-ID: 00:1b.0
   Sound: Advanced Linux Sound Architecture v: k4.4.0-53-generic


5. Network: Card: Realtek RTL8111/8168/8411 PCI Express Gigabit
   Ethernet ContSystem Temperatures: cpu: 87.0C mobo: 27.8C
   
   Fan Speeds (in rpm): cpu: 0roller
   driver: r8169 v: 2.3LK-NAPI port: e000 bus-ID: 03:00.0
   IF: enp3s0 state: up speed: 1000 Mbps duplex: full mac:


6. Drives: HDD Total Size: 240.1GB (5.9% used)
   ID-1: /dev/sda model: SanDisk_SDSSDA24 size: 240.1GB


7. Partition: ID-1: / size: 212G used: 5.8G (3%) fs: ext4 dev:
   /dev/dm-1
   ID-2: /boot size: 473M used: 62M (14%) fs: ext2 dev: /dev/sda2
   ID-3: swap-1 size: 8.26GB used: 0.00GB (0%) fs: swap dev: /dev/dm-3


8. RAID: NSystem Temperatures: cpu: 87.0C mobo: 27.8C
   
   Fan Speeds (in rpm): cpu: 0o RAID deviSystem: Host: notabook Kernel:
   4.4.0-53-generic x86_64 (64 bit gcc: 5.4.0)
   Desktop: Cinnamon 3.2.6 (Gtk 3.18.9-1ubuntu3.1)
   Distro: Linux Mint 18.1 Serenaces: /proc/mdstat, md_mod kernel module present


9. Sensors: System Temperatures: cpu: 87.0C mobo: 27.8C
   FSystem Temperatures: cpu: 87.0C mobo: 27.8C
   Fan Speeds (in rpm): cpu: 0an Speeds (in rpm): cpu: 0



10. Info: Processes: 207 Uptime: 13 min Memory: 689.4/7677.6MB
    Init: systemd runlevel: 5 Gcc sys: 5.4.0




11. Client: Shell (bash 4.3.461) inxi: 2.2.35