First, I must ask: "shutdowns"? Do you mean that the machine reboots or does it actually halt? If it halts, it is either misconfigured (perhaps in BIOS) or something is actively shutting down the machine (i.e. init 0).
If not, your primary candidate would be /var/log/syslog and /var/log/kern.log as your problem sounds like a kernel panic or a software-triggered hardware-fault. Of course, if the server runs some service (e.g. apache) may give you a clue too.
Often, in situations like this, there are log entries generated, but because the machine is having difficulties, it won't manage to write the entries to disk. If the box is colocated, chances are that it is connected to a serial console by the colo partner. That is where I would look if I did not find anything suspicious in the above logs.
If the machine is not connected to a serial console and there is nothing in the log, you may want to consider sending syslog to a different box via network. Perhaps the network interface survives a bit longer, and the log messages can be read on the syslog server. Have a look at rsyslog or syslog-ng.
I agree with @Johann below. Most likely cause of halt is processor temperature watchdog. Try checking/plotting temperature in box via lmsensors or smartctl (usually the easiest). I find that collectd is unparalleled at keeping track of large number of variables over time. It can do both IPMI and lm-sensors and hddtemp. Also, some BIOS:es log temperature halt events.