I've used a seedling mat for bottom heat to encourage root growth along with diluted rooting hormone. How long it takes for root growth really depends on a lot of conditions (how healthy your orchid is, the growing conditions you are providing, etc).
I have a phal that had root rot from sphag not drying out. I repotted into a different medium back in January, only to find that the medium I used was starting to break down and had to repot into something else again in March. I thought all this repotting was going to really set it back, because it had to readjust to new medium each time. I checked on it every time I watered to see if there were any changes and saw none. There wasn't growth yet the leaves and roots seem to be the same. However just today when I watered it, I saw through the clear pot that the current roots branched off with new roots, and there is a tiny nub within the leaves that might be a new spike! Meanwhile I have a den that just decided to bounce back and give me new roots in a week. I think it really all depends! Hang in there!