If your 1-year-old baby has been sweating a lot but not running a fever for less than a week, there are a few things you can try. Keep your baby well hydrated, dress them in light clothing, wipe them with lukewarm water, maintain a comfortable room temperature, and continue monitoring their temperature. If your baby shows signs of being very irritable, sleepy, coughing, or wheezing, it's best to consult a doctor.