This paper reports the first known investigation of power dissipation and electrical breakdown in aerosol-jet-printed (AJP) graphene interconnects. The electrical performance of aerosol-jet printed (AJP) graphene was characterized using the Transmission Line Method (TLM). The electrical resistance decreased with increasing printing pass number (n); the lowest sheet resistance measured was 1.5 kΩ/sq. for n = 50. The role of thermal resistance (R_TH) in power dissipation was studied using a combination of electrical breakdown thermometry and infrared (IR) imaging. A simple lumped thermal model (ΔT=P×RTHΔT=P×RTH) and COMSOL Multiphysics was used to extract the total R_TH, including interfaces. The R_TH of AJP graphene on Kapton is ~27 times greater than that of AJP graphene on Al₂O₃ with a corresponding breakdown current density 10 times less on Kapton versus Al₂O₃.