Conclusion
Sweating out cold by any means you choose, whether exposure to heated air or exercise does not hurt, it also does not cure a cold. However, it may help temporarily relieve you of some symptoms. There is no exact cure for a cold. You would have to allow your body to fight the virus off, which could take up to ten days. Staying hydrated, getting enough rest, and using OTC medications can help ease the symptoms.
References;
[1] https://www.healthline.com/health/nasal-congestion
[2] https://my.clevelandclinic.org/health/symptoms/10880-fever
[3] https://medlineplus.gov/painrelievers.html
[4] https://www.nhs.uk/conditions/decongestants/
[5] https://www.medicalnewstoday.com/articles/expectorants