Why does my CPU temperature read so high?

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Hello sexy penguins,

I'm concerned about my CPU - it's reading at 127.5 C pretty much constantly, idle or otherwise. I've followed recommended procedure for applying Arctic Silver 5 twice to no avail and the heat sink and fan air are cool. Stranger still, my mobo BIOS (MSI Z97I AC) reads 70 C in BIOS, which is still high but much lower and within Intel's rec'd operating temps. I've read that lm_sensors lets you offset temps to keep alarms from triggering, but I would really like to know what the true temp is, if possible. I've also read that the sensors themselves are a rare point of failure.

Sensor readings as follows

coretemp-isa-0000

Adapter: ISA adapter
Package id 0:  +36.0°C  (high = +80.0°C, crit = +100.0°C)
Core 0:        +33.0°C  (high = +80.0°C, crit = +100.0°C)
Core 1:        +32.0°C  (high = +80.0°C, crit = +100.0°C)
Core 2:        +36.0°C  (high = +80.0°C, crit = +100.0°C)
Core 3:        +33.0°C  (high = +80.0°C, crit = +100.0°C)

acpitz-virtual-0
Adapter: Virtual device
temp1:        +27.8°C  (crit = +105.0°C)
temp2:        +29.8°C  (crit = +105.0°C)

nct6779-isa-0a10
Adapter: ISA adapter
Vcore:                  +0.90 V  (min =  +0.00 V, max =  +1.74 V)
in1:                    +1.02 V  (min =  +0.00 V, max =  +0.00 V)  ALARM
AVCC:                   +3.39 V  (min =  +2.98 V, max =  +3.63 V)
+3.3V:                  +3.39 V  (min =  +2.98 V, max =  +3.63 V)
in4:                    +1.11 V  (min =  +0.00 V, max =  +0.00 V)  ALARM
in5:                    +0.80 V  (min =  +0.00 V, max =  +0.00 V)  ALARM
in6:                    +1.06 V  (min =  +0.00 V, max =  +0.00 V)  ALARM
3VSB:                   +3.39 V  (min =  +2.98 V, max =  +3.63 V)
Vbat:                   +3.30 V  (min =  +2.70 V, max =  +3.63 V)
in9:                    +1.01 V  (min =  +0.00 V, max =  +0.00 V)  ALARM
in10:                   +0.01 V  (min =  +0.00 V, max =  +0.00 V)  ALARM
in11:                   +0.00 V  (min =  +0.00 V, max =  +0.00 V)
in12:                   +1.01 V  (min =  +0.00 V, max =  +0.00 V)  ALARM
in13:                   +0.74 V  (min =  +0.00 V, max =  +0.00 V)  ALARM
in14:                   +0.84 V  (min =  +0.00 V, max =  +0.00 V)  ALARM
fan1:                  1153 RPM  (min =    0 RPM)
fan2:                  1021 RPM  (min =    0 RPM)
fan3:                     0 RPM  (min =    0 RPM)
fan4:                     0 RPM  (min =    0 RPM)
fan5:                     0 RPM  (min =    0 RPM)
SYSTIN:                 +34.0°C  (high =  +0.0°C, hyst =  +0.0°C)  ALARM  sensor = CPU diode
CPUTIN:                +127.5°C  (high = +80.0°C, hyst = +75.0°C)  ALARM  sensor = CPU diode
AUXTIN0:                +23.0°C    sensor = thermistor
AUXTIN1:               +127.0°C    sensor = thermistor
AUXTIN2:               -128.0°C    sensor = thermistor
AUXTIN3:                -60.0°C    sensor = thermal diode
PECI Agent 0:           +34.5°C  
PCH_CHIP_CPU_MAX_TEMP:   +0.0°C ...