Take them to the floor. As long as the heater isn’t electric, the baseboard heat cover doesn’t get hot enough to be of concern.

You need 350*-450* of iron heat just to get rid of wrinkles in fabric.

just a word of warning: even if the curtains are above the heater, some of the heat will rise, get trapped under and not circulate into your room. if this heater is already inefficient, this will make it worse. (trust me, I learned this from experience and a very cold apartment.)

baseboards are the worst to design around. sorry!

The 84 inch ones would look worse to me than the 63. The 63s would look better if they ended at the apron.

I would avoid the problem by not putting up the curtains. Could you settle for a boxed valance covered in the fabric of the drapes?

You have a nice, modern, clean look there now.

A Roman blind might look nice there too.

If it's electric, it needs to be at least 10" above the heater, minimum. If it's not electric, I'd take it to the floor. Anything shorter doesn't look good IMO. If you're just wanting to add some fabric, maybe a faux roman or even an outside mount working roman.

We have a second home with similar heaters and one was in an odd location. The heaters have the knob on the left or on the right , and that corresponded to where the wires were coming out of the wall. We were able to swap a left knob heater with a right knob heater, freeing up wall space for a dresser or something - I dont recall what. There wasnt anything really involved with the swap - our heaters are held in place with two screws. Also - there are new replacement heaters, that are more of a flat rectangle. If your wires are by your knob, you may be able to put a new flat replacement version between two long panels. Then you just need to keep the panels open. For our windows with heaters below - the curtains are maybe 6” longer than the bottom of the window and in the winter when the heaters are on we tuck the fabric up on to the sill and they are held in place with the blinds. Because heat going up curtains is a whole other problem :)

If you can't go the floor because of the heater I would do an outside mount roman shade. Curtains that are too short never really look right. Are there other windows in the room? I would consider upgrading the blinds as well.

I like the roman shade idea. there are so many styles, some more modern and some more classic. inside or outside mount.

good quality cellular shades look nice and can cut down on heating bills (since baseboards tend to be electricity hogs):

We have electric baseboard heat in our family room. we hung curtains about 8 inches above the heater. On the window without the baseboard heater, we hung the curtain the same height at top and bottom as the other one and looks fine, Might not be correct but there is a reason for it and has to be done that way.

Have an HVAC/Electrician come in to determine what it would cost to move it so that you can hang curtains properly...Good Luck!

Maybe consider a baseboard heater cover for a more finished look. I think shorter curtains then won‘t feel as awkward, but for an even nicer look, you could add new blinds, a bench under window for interest and balance and if heating is only under window, add decorative drapes on the sides