The baby's (rectal) temperature is 37.6. Is that high or normal? His cheeks are very red and I suspect a fever because he's also a bit more irritable.

A rectal temperature of 37.6 degrees Celsius is considered normal for a baby. Fever in babies is typically defined as a temperature equal to or greater than 38.1 degrees Celsius for infants under 3 months old, and 38.5 degrees Celsius for infants over 3 months old. If your baby's cheeks are very red and they seem more irritable than usual, it may be a sign of a fever.