Unruh radiation and conservation of energy Consider the Minkowski spacetime filled by some fields in their Minkowskian vaccum state. Now consider a Rindler observer carrying with him, say, one liter of water. According to Unruh formula, the water should heat up (imagine a huge acceleration). Where does this energy come from? It can't come from the vaccum sate, because, by definition, it is the state of lowest energy, and thus can't loose more energy!
First element of answer: rinder observers are eternally accelerated. So the thermal equilibrium exists from the beginning (past infinity), and there is no heating up of the water, it is already heaten.
Ok then, consider an observer accelerated for a finite amount of time. Though it may still be controversial, some authors claim that a kind of Unruh effect exists here as well (eg. diamond temperature, Rovelli, arxiv). Then the question makes sense: the water does heat up during the process, and must take the energy from somewhere. 
From where? Padmanabhan in some papers say "it takes the energy from spacetime itself", which is obscure enough...
 A: The original Unruh & Wald (1983) paper addresses precisely this question. (You can find it here: http://www2.kau.se/tp/marcus/physics/lectures/unruhwald.pdf.) They discuss measurement of the thermal radiation by the accelerated observer via a two-state system, where the system jumps to a higher energy level on absorbing a quantum of the thermal radiation. This is the analog of your liter of water. 
What the accelerated observer views as the absorption of a thermal quantum along with the excitation of the detector, the inertial observer views as the emission of a quantum, along with the excitation of the detector. As cesaruliana says, the energy came from whatever keeps the system accelerating (from the inertial standpoint).
For the accelerated observer, the energy comes from a fundamentally quantum phenomenon, namely what they refer to as a "partial measurement" of the field state. The fact that the detector was excited means that the corresponding mode of the field was likely to be populated by many quanta (=> higher probability of producing the excitation). So the excitation of the detector raises the expectation value of the energy in the corresponding mode. 
A: Based on what J Richard Gott writes in " Time Travel and Einstein's Universe" , the vacuum energy density  at the point of Unruh radiation absorption is equal and opposite in sign to the Unruh radiation density. In the accelerated frame, vacuum energy density is negative. It has been mentioned above that  the energy for Unruh radiation can't come from the vacuum because the vacuum is at its state of lowest energy. But there is no such bound from below in QFT for the vacuum state. Were there such a bound black holes could not evaporate, the vacuum around the event horizon violates the weak energy condition.  
