Heat is actually more concerning than power usage when it comes to data centers -- If the silicon heats up too much, the chip becomes unreliable, and we end up spending a lot of money on cooling the data centers anyway.
Mobile devices have the ability to dissipate heat along the phone case that normally surrounds the phone, which is one reason why we don't have fans inside our phones. Also, I would guess the computational power for phones is just less than it is for laptops (which normally do have fans).
@totofufu This is almost always the case. If the phone and laptop is from the same generation, the laptop will almost always beat the phone in direct performance. Of course, this isn't always true for Chromebooks which also usually run ARM processors like almost all phones, but even for the newer fanless ultrabooks, which still run x86 intel processors, phones simply don't provide the same performance.
On the note of datacenters, heat (and consequently power) is a real concern because beyond performance and cost based issues, too much heat leading to datacenters going on fire, as shown here can also occur, with more devastating consequences.
Could someone explain what it means for the silicon to become unreliable? And does it also mean once it is cooled, it becomes reliable again? What happens while it is unreliable?
You want registers to represent at least the same value within a clock cycle. Registers can be made of combination of logic gates, which is made in silicon. When temperature is higher than some threshold, the logic gates don't output reliable results anymore.
@althalus to add on to the other answer, in rare situations, excessive amounts of heat could cause permanent damage, but in most cases, once it is cooled, yes it become reliable again.
The idea is that, there cases where a bit will be erroneously flipped in a register or even the RAM. The probability is extremely low, but it increases significantly when there is too much heat because the electrical properties begin to change past a certain temperature. So when it is too hot, there will be errors in the computation, which obviously we want to avoid.
The introduction of SSD's into data centers has significantly improved power and heat issues, however power is probably the biggest drain on a Datacenter cost wise. Most datacenters have a really cool negative or positive pressure system going, where the air is either forced through the server racks from the inside, or from the outside. However such systems just add to the costs of power.