Any experience with baby 4 months plus old and having fever up to 39 degrees. What will you recommend to do, other than sponge and medicine?

I would rush her to a PD as a fever of 39 degrees is extremely high for even adults, much less babies. For infants below 6 months of age, anything above 37.5 deg Celcius should warrant medical attention. http://sg.theasianparent.com/treating-your-babys-fever/