The current springs I am planning on would be for a matchlock build, so they would be far simpler and more forgiving than a flintlock mainspring. I have some options to avoid making springs, but I was considering the possibility to help learn the skills for future projects.Well, the responses were about what I expected. Listen to Wick (LRB) as he is the only one here that I know- knows his stuff. I was going to suggest brine but from your original question of being in cramped quarters and no space for a big set up- I thought I'd keep it as simple as possible.
I make springs for folding knives and the stress is probably a lot less than than a main spring for a lock on a gun. Actually, I wouldn't suggest a newbie try to make a main spring for a gun lock- buy that.
On the refractory type brick- Wayne Goddard sold a book- the $50 knife shop. It had the one brick forge. I did that, forged blades, etc.- just using a propane torch, in fact that's the set up when I got the blade up to yellow and burnt out all the carbon. But- you don't need to do that. You can hold the metal in thongs and heat with a propane torch although a shelter area of fireproof material in which the metal is placed would probably be better.
In any event I've made springs as I described with propane, no special bricks, just heat as I said. Since brine has been mentioned- use that, This isn't a life and death kind of thing- I hope. Play around with it, on the color, I work in an enclosed area with low light so a heated metal shows more color than in a better lit area. You learn by doing, so try some springs- test until they bend, break, or fail. Quenching to a brittle temper isn't so hard, drawing it until you get to the spring temper, that's what you ought to focus upon. You polish to get the color spectrum.
What is your preferred method to temper?