What is claimed is:1. A processing unit comprising:a first die;a second die;a microfluidic volume between the first die and the second die, the microfluidic volume configured to receive an electrochemical fluid flowing through the microfluidic volume;a membrane positioned within the microfluidic volume configured to separate an anolyte fluid and a catalytic fluid of the electrochemical fluid; anda heat transfer structure coupling the first die to the second die and located in the microfluidic volume.2. The processing unit of claim 1, wherein the electrochemical fluid is an anolyte fluid, and a catholyte fluid is separated from the anolyte fluid by a membrane.3. The processing unit of claim 2, wherein the membrane and catholyte fluid are located in the microfluidic volume.4. The processing unit of claim 3, wherein the heat transfer structure is the membrane.5. The processing unit of claim 4, wherein the heat transfer structure divides the microfluidic volume into at least a first channel and a second channel,wherein the anolyte fluid is located in the first channel and the catholyte fluid is located in the second channel.6. The processing unit of claim 5, wherein a cross-sectional area of the first channel varies along a length of the first fluid channel.7. The processing unit of claim 5, wherein the heat transfer structure is curved in a direction of flow of the anolyte fluid.8. The processing unit of claim 2, wherein at least part of the membrane includes the second die.9. The processing unit of claim 1, wherein the heat transfer structure includes a plurality of pin fins.10. The processing unit of claim 1, further comprising a charging device in fluid communication with the microfluidic volume and configured to recharge a discharged electrochemical fluid with a power source after the electrochemical fluid provides electrochemical energy to at least one of the first die and the second die.11. The processing unit of claim 1, further comprising a heat exchanger in communication with the microfluidic volume and configured to exhaust heat from the electrochemical fluid.12. The processing unit of claim 1, wherein the microfluidic volume is a first microfluidic volume and the processing unit further comprises a second microfluidic volume proximate the first die and opposite the first microfluidic volume, and wherein at least a portion of the electrochemical fluid is positioned in the second microfluidic volume to provide electrochemical energy to the first die and receive heat from the first die.13. A computing system comprising:a first wafer including:a first die,a second die,a first microfluidic volume between the first die and the second die, anda first plurality of heat transfer structures coupling the first die to the second die and located in the first microfluidic volume;a second wafer including:a third die,a fourth die,a second microfluidic volume between the third die and the fourth die, anda second plurality of heat transfer structures coupling the third die to the fourth die and located in the second microfluidic volume; anda manifold configured to flow an electrochemical fluid through the first microfluidic volume and the second microfluidic volume, the electrochemical fluid configured to provide electrical power to the first die and second die and to receive heat from the first plurality of heat transfer structures and the second plurality of heat transfer structures.14. The computing system of claim 13, wherein the heat transfer structures include straight fins.15. The computing system of claim 13, further comprising through-silicon vias (TSVs) electrically connecting the first die to the second die.16. The computing system of claim 15, further comprising TSVs electrically connecting the third die to the fourth die.17. The computing system of claim 13, wherein a first flow direction of the electrochemical fluid through the first microfluidic volume is opposite a second flow direction of the electrochemical fluid through the second microfluidic volume.18. A method of providing power and cooling to a stacked-die processor, the method comprising: providing an electrochemical fluid to a microfluidic volume of the stacked-die processor;using the electrochemical fluid, generating electrical power at the stacked-die processor;receiving heat from the stacked-die processor with the electrochemical fluid in the microfluidic volume; andexhausting the heat from the electrochemical fluid at a heat exchanger.19. The method of claim 18 further comprising recharging the electrochemical fluid at a charging device.20. The method of claim 18, wherein generating the electrical power at the stacked-die processor with the electrochemical fluid includes transferring ions across an ion-transfer membrane located in the microfluidic volume.