The slitting saw is a milling cutter. Calculate rpm, feeds and chip loads just like any other milling cutter. There are just more teeth to count! If things are getting hot that implies a lot of friction. Might be a feedrate problem. Feedrates for slitting saws are proportionally quite high, as there are a lot of teeth.
Don’t bother with fine pitch slitting saws, unless you are doing a lot of shallow depth cuts such as slotting screw heads. The gullets clog up too easily.
Rules for coolant follow those for milling other materials, nothing special about slitting saws.
If the mounting arbor has a slot for a drive key, don’t use one. If it all goes pear-shaped you want the cutter to slip on the arbor, not shatter.
My experience has been that on a stub mandrel on a vertical mill, there is a tendency for the slitting saw to wander off on cuts deeper than the few millimetres. On a big horizontal with outboard arbor support, no such problems.
Last but not least, whatever you do, and no matter how perfect everything is, the slitting saw will not cut evenly on all teeth. Don’t worry about it.
Regards,
Andrew