I make hot fudge syrup ; heat chocolate , sugar , butter, etc, to 240 F ,then put in half and half . I end up with a spoon-able viscosity at room temperature but warming to 100 F makes it pour-able. Does it make any difference how fast I heat it ? I don't need it to firm up into fudge.
The limiting factor for how fast you can heat your syrups is how evenly that heat is distributed through the liquid. If you have a runny liquid, a thick pot that distributes well and you stir constantly, you can heat very fast. The heated liquid is immediately mixed throughout.
On the other hand, if your syrup is viscous it won't mix easily. If your pan is thin then there will be hot spots. The syrup will get too hot and burn at those points.
Another consideration is precise temperatures needed for candy making. If your syrup is destined for a denser candy then you want to hit a final temperature that is within about a 5F range. It might be hard to hit accurately if you are heating too fast.
Personally, I start my syrups on medium-medium low until the sugar is dissolved and then bump the temp up to almost high. If I'm making candy I'll go back to a medium high when it starts getting close.
As for reheating- just use a microwave. The syrup won't burn.
Some recipes need to be heated gently. Eggs, for example, are more likely to curdle when they are heated abruptly- even if they are only heated to the same temperature.
This does not apply to sugar syrups.