Combine FFT's of shorter length than sample data to get spectrum of all data

I have a set of sample data, a logarithmic swept sine as it happens, that is 1 second in duration sampled at 100kHz giving 100k samples. I want to calculate the frequency spectrum of the complete data however the FFT library function available only supports 4096 samples maximum.

Is it valid to sequentially FFT 4096 samples and sum the resulting data. Thereby ending up with 4096/2 frequency points that show the frequency content of the entire 100k samples?

I guess it is necessary to window each block of 4096 samples to be FFT'd but this would mean that the portions of the frequency content would be reduce in amplitude artificially.

How does one handle the phase information?