So far, the high Tc transition edge bolometer (TEB) devices are mostly used as single pixel detectors. Recently, there are a number of groups working on the 2-4 pixel array applications of the high Tc TEB. Though the target spectrum of the TEB is far IR and mm-waves, we are using a near IR laser source in our investigation due to practical reasons since the response analysis is similar. We have designed and implemented 4-pixel Y Ba2Cu3O7−δ (YBCO) edge transition bolometer arrays. The crosstalk study was made possible through the illumination of the sense-devices and measuring the voltage response of the blocked read-out device in the same array. This was done using a silver coated shadow mask. In order to prevent thermal artifacts created by the mask, the mask was made in free standing configuration on top of the devices. The devices were made of 200 nm and 400 nm thick pulsed laser deposited YBCO films on SrT iO3 and LaAl2O3 substrate materials. In this thesis, we made the qualitative investigation of the dependence of the thermal crosstalk on the various device parameters such as the substrate material, device layout, YBCO film thickness, operating temperature, and modulation frequency. Then, based on the experimental results, we proposed an analytical thermal model. We proposed two models: i) Basic model, which takes into account only the lateral heat diffusion in the substrate for quick design purposes ii)Analytical model, which takes into account the lateral heat diffusion, vertical heat diffusion, and the effect of the leaking laser radiation through the shadow mask, for detailed design purposes and verifying the qualitative analysis. Finally, we proposed and verified possible applications of the thermal crosstalk in TEB arrays. One proposed application of the crosstalk is the electrical free read-out of the sense pixels by utilization of the unique dependence of the magnitude and phase of the response on the thermal crosstalk between bolometer pixels in an array. The qualitative investigation made in this study is the most detailed investigation about the bolometer arrays and the proposed analytical model is the strongest among the reported ones so far in terms of fitting the experimental results, explaining the effects of the various parameters, and designing TEB arrays. The proposed crosstalk based read-out method is expected to decrease the read-out circuitry for possible TEB based applications. Since multilayer process is difficult to make in high Tc superconductors, decreasing the complexity of the read-out circuitry by half is even important and it is the first time that such a method is utilized including bolometer arrays made of different types of materials.