This thesis starts with an introduction to the background semiconductor physics required for carrying out this PhD research. I have then presented the work that demonstrates, both theoretically and experimentally, an energy harvester built from two resonant-tunnelling quantum dots. A device, proposed by Jordan et al. [1], harvests energy from an area of 90 μ m2 of a two-dimensional electron gas (2DEG), using the energy-selective transport of electrons through a pair of quantum dots. It has proven to be an effective technique for harvesting energy at the micro/nano scales. Our energy harvester can generate a power of 0.13fW in an estimated efficiency with a lower bound around 0.1hC. Our theoretical model (not affected by limitations of the Wiedemann- Franz law) suggests the actual efficiency to be about 0.5hC. Experimental observations of thermal power, voltage and efficiency at different values of IHeat and RLoad have also been reproduced by this model. There are small quantitative differences between experimental results and theoretical modelling in terms of parameters, such as electrical temperatures and energy level difference. This may be explained by asymmetric barriers, accidental degeneracies or the lifetime-broadened width of the quantum dots, as well as charging effects in the non-linear regime. Overall, this proof-of-principle experiment demonstrates the basic soundness of the theory of mesoscopic energy harvesting with energy filtering techniques at the quantum level, realising a heat engine. Then we investigate the thermometry study of such a quantum-dot energy-harvester device. This part of the thesis describes the characterisation and performance of a non- invasive single-electron thermometer, and extracts the electrical temperatures via three methods as below. First, we introduced the extracting of the electrical temperatures through fitting the differential-conductance peaks with theoretical models. The advantage of this method is that the quantum dot can directly serve as a thermometer. The disadvantage is that the excitation voltage, applied to trigger the currents through quantum dots, will unavoidably heat the device. Then we introduce the use of the quantum point contact (qpc) to extract temperatures via monitoring the changes in electrostatic potential of a one-dimensional channel close to the quantum dot. It is easier to set up this measurement, and the signal through a qpc is usually several times greater than the current through a quantum dot, which means that the qpc thermometer is much more sensitive than the quantum-dot thermometer for a similar experimental set-up. The third method is to use the Mott relation as an insight into the thermometry of our energy-harvester device. It is supposed to have higher accuracy compared to previous thermometers, because of the same sets of circuits and data used as the thermopower measurements. Then I have presented our attempt to experimentally demonstrate the theoretical proposal of building an energy harvester with two resonant-tunnelling quantum wells by Sothmann et al. [2]. This can scale up the quantum-dot energy harvester, increase its working temper- ature and the generated thermal power. The design and fabrication process have also been presented in detail. Measurements has proven that the split-gate and mid-gate combination can successfully give us access to each individual layer. This work can be improved by fabricating such an energy-harvester device with a double-quantum-well wafer with a narrow barrier width. Both devices discussed in this thesis require a good thermal contact to two-dimensional electron gases. The electron temperatures are key to study their power and efficiency, and therefore it is important to study the thermometry of corresponding measurements.