The man's ventilator then ran out of power 30 minutes later.
The family alerted medical staff who performed CPR, however it was not enough to save the man.
Hospital superintendent Dr Naveen Saxena said they will be investigating the incident surrounding the patient's death.
The doctor said action would be taken against whoever is found responsible in the probe report.
The family members allegedly did not seek permission to plug in the cooler and when the patient died, they "misbehaved" with the medical staff and the resident doctor on duty, the hospital authorities said.