BQ78350-R1: Issue, CHG and DSG FET off when CUV, COT

Hi Jaroslaw,
It is common for a pack to heat as discharged, particularly if the discharge is at high rate. Be sure to design adequate thermal management in the system if temperature is an issue.
The CUV =1 is an undervoltage condition. For temperature there is the OTC and OTD conditions. OTC is 55 C by default while OTD is 60 C by default, so it is possible a pack could heat during discharge to prevent charge. If the value has returned to 0 the pack must have cooled below the OTC recovery of 50 C, and this condition would not be blocking charge.
Notice that the CUV operation described in the technical reference manual (TRM) section 3.2 is different from the precharge operation in section 5. The thresholds and recovery thresholds are different. Also be sure you have the proper FET selected for the precharge condition. If your circuit design does not implement a precharge FET but the configuration is set for one, the pack will not be able to charge.
Check the thresholds and the FET Options[PCHG_EN] bit selection in the parameter configuration. A log file should allow you to see what is happening as the voltage drops, temperature rises and the mode and status of the pack change. Monitoring after status should show the recovery and which FETs are enabled.