You can preheat to 250 oC, weld it using 1CrMo or Mild Steel (G3Si1 or similar), and then ideally pwht at 400 OC for a hour per inch thickness. You can temper at a higher temp if you want it softer.
Alternatively you can try to do without preheat (but not cold) and use an austenitic stainless 309L or 312
It will be uncomfortable but TIG is probably the best process
As you are joining it to MS I would go for the preheat and MS wire but its your choice.
It really depends if you want to heat treat the H13 after welding
I'm guessing it's related to this thread? http://www.mig-welding.co.uk/forum/showthread.php?t=35967 which'd make the h13 already hardened? Do we know how hard (tempering temperature etc)? The link TechnicAl posted last time covers most scenarios just as he did here and, as said, you need to know what's gonna be done to it after your finished