This chapter explores the emergence of correlated states in Hall chiral quantum systems, focusing on their impact on thermal and electrical transport. We analyze a setup where an Ohmic contact is connected to multiple edge states, with one forming a loop. Surprisingly, this looped edge state carries more heat than expected in equilibrium, an effect linked to charge fluctuations in the Ohmic contact. To probe this phenomenon, we consider two types of thermometry: capacitive coupling and quantum point contacts (QPCs). While a capacitive probe fails to detect excess heat in equilibrium, a QPC reveals a fundamental violation of the Wiedemann-Franz law, which means the ratio of thermal to electrical conductance deviates from its expected universal value. This violation depends only on the resistance of the circuit and persists in various temperature conditions. We further analyze how heating the Ohmic contact affects transport and confirm our predictions through numerical calculations. The findings connect to broader physics, including Tomonaga-Luttinger liquids and fractional quantum Hall systems, offering new insights into heat transport and fluctuation effects in chiral electronic systems.