Caution - If the following paragraph makes your head hurt, skip to the next section.
When the steel is quenched it is austenite , because it was heated above the critical or As point and held at the target or Af point.
It becomes super-cooled austenite in about one second if you did the quench right. Now, austenite is a real soft structure. It can easily be bent and twisted. It does not get hard until it reaches the martensite start point (Ms)...about 400F. Even then the steel has some percentage of austenite in it. The level drops until it is all martensite at the martensite finish point (Mf).....on most simple carbon steels ,that is around 200F. Thus, any straightening above 300F will be safe and easy to do. Once the steel starts to stiffen up, it becomes brittle martensite, and will snap like glass with any twist or flex. At this point stop all attempts to straighten the blade. It will need to be tempered to make the brittle martensite into tempered martensite before any more straightening can be done. The ability to be bent without breaking is greater at the temper point than room temperature, so doing the straightening right out of the oven is when the remaining bends/twists should be removed. If the blade cools down, just stick it back in for five or ten minutes to heat it up again and continue straightening until satisfied. You can do this as many times as needed and it will not affect the temper at all. Once done, dunk in water and check one final time.
I am going to digress from the straightening info for a second here and state that it is actually better to cool from tempering to room temp by just sticking the blade in water or rinsing in the sink under the faucet. There are a few metallurgical things that happen a tad better by quickly cooling to room temp from the temper point. It will not make a blade warp or break. If you want to let it cool slowly, that is fine, but a water cooling is technically better.
Now, for the brain friendly stuff - The methods of straightening are :
Use gloved hands - You don't want the mittens Mom makes you wear when it is cold. You need heat resistant "Heat treatment" gloves. I have an ancient pair of Asbestos foundry gloves on the wall ( in a plastic bag) to remind me how good these used to be. Today, they resist heat fairly well, but aren't totally heat proof, so be prepared for some hot finger tips.
Pull the blade out of the quench after about ten seconds. Wipe it off quickly with a rag and sight down the blade ,checking for warp and twist. Straighten any bends by hand immediately.
Use a straightening board - Have a slotted piece of 2X4 clamped in the vise. The slot should be as deep as the blade is wide, and a tad wider than the blade thickness. Slip the blade in the slot and twist/bend as needed. this is fast and easy, and can be done while holding the blade in tongs or vise grips. Note - never grip the hot blade with pliers or vise grips anywhere but the tang, as they will leave a mark in the soft austenitic steel.
An alternate method is to quickly clamp the tang in the vise and use the slotted board in your hands to bend/twist the blade as needed.
If you just use the vise jaws to straighten the blade, you will speed up the cooling and it can snap. You can also put marks in the soft blade from the vise jaws.
Use a "schwacker" - A schwacker is the technical term for a wooden straightening hammer.....OK, it is just what I call it, but most smiths have one.
Make a straightening hammer out of any hard wood you wish. Many just use a 12" piece of a broken base ball bat.
It can be a club type schwacker, or a mallet type....doesn't matter. The anvil needs a wooden face on it.This is called the "schwackenplank"
. Cut a piece of oak or other wood and add some cleats or something so it stays in place on the anvil face. The reason for the wooden parts is that they don't speed up the cooling of the blade as fast as a metal hammer and anvil will. They don't make dents as badly, either.
To use the schwacker, just pull the hot blade from the quench and pound out any warps present.