Maybe. You will externally fire a radiant tube, and inside the tube will be your crucible of Ti.
Do you really think that you have the burners, fuel, and insulation to reach 3200F?
How low of oxygen are you looking to reach?
Finding the right refractories will be a challenge also.
I suspect this problem has been solved previoulsy and there is benefit to avoiding "reinventing the wheel". Most titanium is sourced from Russia, so one might want to review how they produce the bulk metal.
it is possible that the material is melted and refined using a plasma arc and not using a direct fired combustion flame. It is also possible that the trace elements that may pollute the melt can originate from direct combustion byproducts.
"...when logic, and proportion, have fallen, sloppy dead..." Grace Slick
EBM and Arc are the main method to melt down high melting-point metals. Induction is possible too, although to the border line (people use VIM to melt Ti alloy). The biggest concern is the crucible reactions. Ti is very reactive, it will react with almost any ceramic crucbile (Al, Si Zr,Ca oxides. oxygen control is a big deal.
Graphite maybe a choice. Often, people use crucible less melting (e.g. water-cooled cu crucible) to prevent crucible contamination.