200 is the target temp for the dye. I have done handles the way you did with good results. 30 minutes each end should be plenty. I would make sure to use the Synthetic RIT dye called Graphite color. Don't use the standard black regular rit dye.
The other thing is, once it is done and fully dried (wait a day at least), wipe it down with some good automotive vinyl protectant. I use Aerospace 303 but others should work ok as well. That brings back the nice rich sheen to the plastic.
I also welded up a custom rectangular SS bin that I use to dye my parts and use a turkey fryer to heat up the solution. It allows me to lay the handles down fully in the solution so I don't have to do one end at a time. I am planning to do some dyeing later this summer and will do several handles along with knobs and igniter switches. It is kind of an involved process and I don't want to be doing it very often. After that, I will be doing a lot of "Black Out" edition Silver B rehabs.....hahaha