In recent years increasing evidence has emerged for a thermal component in the \gamma - and X-ray spectrum of the prompt emission phase in gamma-ray bursts .
The temperature and flux of the thermal component show a characteristic break in the temporal behavior after a few seconds .
We show here , that measurements of the temperature and flux of the thermal component at early times ( before the break ) allow the determination of the values of two of the least restricted fireball model parameters : the size at the base of the flow and the outflow bulk Lorentz factor .
Relying on the thermal emission component only , this measurement is insensitive to the inherent uncertainties of previous estimates of the bulk motion Lorentz factor .
We give specific examples of the use of this method : for GRB970828 at redshift z = 0.9578 , we show that the physical size at the base of the flow is r _ { 0 } = ( 2.9 \pm 1.8 ) \times 10 ^ { 8 } Y _ { 0 } ^ { -3 / 2 } cm and the Lorentz factor of the flow is \Gamma = ( 305 \pm 28 ) Y _ { 0 } ^ { 1 / 4 } , and for GRB990510 at z = 1.619 , r _ { 0 } = ( 1.7 \pm 1.7 ) \times 10 ^ { 8 } Y _ { 0 } ^ { -3 / 2 } cm and \Gamma = ( 384 \pm 71 ) Y _ { 0 } ^ { 1 / 4 } , where Y = 1 Y _ { 0 } is the ratio between the total fireball energy and the energy emitted in \gamma -rays .