I'll add a little physics to the metallurgy here. The explanation below isn't meant to be an exact scientific discussion, but is intended to explain the transfer of energy involved in forging and welding.
A weld is when the two metal surfaces combine into a unified structure. It is basically like having the two melt together along the junction of their surfaces at an grain size level.
This requires enough heat to allow the grains to move and interlock with each other. Further refinement by forging down ( or rolling) increases the unified bond and makes the joint stronger.
Heat is energy, and heating an object is merely the absorption of energy. Bend a coat hanger and it gets hot because you are adding energy in the bend. Compress air rapidly and it gets hot because you added energy to the molecules/atoms. Hammer a bar of steel and you add energy to the grains as you force them together.
In forge welding by hand, it is all a factor of how efficiently you swing a hammer the weight of the hammer, the distance it falls, etc. - For practical purposed a 3 to 4 pound hand hammer is the limit you can effectively swing, and an 8 to 10 pound sledge is all a striker can easily swing.
A power hammer delivers multiple blows with a bigger hammer. They range from 25 pounds to hundreds of pounds in hammer weight. The normal range for knifemakers is 33 to 100 pounds.
A press delivers many tons of pressure, witch is roughly equivalent to a very large hammer. Forging presses usually deliver a fairly quick force of around 40,000 pounds (20 tons). This is a lot of energy, but you only get a few presses at welding heat before the mass drops below the fusion point.
A rolling mill squeezes the metal from both sides and delivers a very intense addition of energy at the rollers. This is the most efficient way of reducing thickness or welding laminated ... but not practical for small shop knifemaking.
If a hammer was big enough, theoretically you could weld at room temp. In practicality, the steel has to be at least 1600°F to weld with a giant hammer or rolling mill.
The range where the atoms can move enough to fuse but not mush the billet apart is roughly 1600°F to 2300°F. For most hand forgers, the upper limit of 2200-2300F is the advised range, For those with a press or power hammer, 2100-2200°F is better. I would suspect that the big places with giant 500 pound hammers and 100 ton presses go down as low as 1800°F.
The sweet spot for welding is a temperature where the steel is still solid enough to survive the pressure of welding, but not so high that the grains slide apart or fully melt. The exact temperature is almost always judged by eye and learned by experience on your set of equipment. The bigger the hammer or press, the lower the temperature of the billet can be. As the hammer or press delivers energy to the billet, the temperature rises. You can see this when forging. As the steel drops to a duller red, strike the bar hard with a hammer. You will notice the color jumps up a good bit at the spot impacted … and quickly drops back to the lower heat color as the energy gets dissipated into the surrounding steel.
All forge welded billets should get grain refinement procedures to lower the grain size. You need to both refine the grain as well as release any internal stress from the welding and reducing procedures. Everyone has their own methods, but they should include reduced cycling temperatures ending in a quench, This is best done as soon as the billet is reduced to the thickness desired and/or the blade rough shaped by forging. These procedures need to be done prior to the hardening quench to assure a blade with internal integrity.
Summation:
Metallurgically, the forging range of most knife steels is between 1600F and 2100F. If steel is in this range the damage to the grain is minimal and correctable. For forging you have enough energy in the steel for the task of moving the grains around to re-shape the billet as needed. For welding you need more energy. Picking a place where the steel's structures are still unaffected but the added energy fuses the weld is what you are shooting for. Start at what you think is the bottom of the range. If you can master that range and get solid welds, your blades will benefit. If the welds aren't solid enough with your methods and equipment, then raise the temperature. The only practical gauge is your eye.
Once the layers are bonded, lower the heat by around 100 degrees to work and solidify the billet. Proper stress and grain reduction should follow the welding and reduction .