Responded to improper cooling call. Turned breakers on for ac and furnace upon arrival and called for cooling. Found system cycled on properly without issue. Ran with 15 degree delta t. Customer stated thermostat wouldn’t turn system off. Ran until house was 57 degrees before customer turned breakers off to system. Technician cycled system through thermostat multiple times without cause for concerns system properly cycled each time. Informed customer does sound like a intermittent thermostat or board issue cannot confirm or deny source of experience however everything is working good at this time. Found dirty condenser also found 3” hole in flue pipe as well as surface rust and holes in metal flu pipe. Informed customer of health hazard and advised it to get fixed before heating season. Customer opted to get replaced today presented option HM13A-E for replacement. Customer chose option a. Technician retrieved needed parts and performed repair. Customer opted to clean condenser themselv