When you reignite a fire in game the temperature of the fire never gets above the starting temperature at the time it's relit. The reignited fire will not give a heat-buff, allow cooking, or dry clothing.
For example, if the fire temperature drops to 100C after going out and at the point it is reignited, the fire will never get above 100C after it's relit. This is regardless of the amount of wood added or how long the fire is kept going. Until the fire completely goes out and is lit from scratch with new kindling and a firestarter, the temperature will never increase.