stiff seacocks (no pun intended)

First thing is frequently exercising them is a big maintenance item. Probably opening and closing every couple of months does wonders.
Have you tried this at least a half dozen times to see if they loosen up.

I'm not sure about them . Maybe one of the Capts' will chime in. There are a few different kind of seacocks .what kind do you have as they are all a little different to service, if they can be serviced at all. Maybe your favorite penetrating oil sprayed on it a few times will help loosen it up over a couple days time.

Work the hell out of them every couple of weeks and see what happens. On the yachts I manage, I work the seacocks monthly.

Grease them . remove the drain plug and install a zerk fitting . Place the valve in a 3/4 open position , give it three or four shots of grease . When greasing make sure the valve is NOT in the fully open or fully closed position , you will damage the inner seals .

Use lithium grease, if you do that.

Lithium is water resistant grease and a light weight, so it should get in all of the crevices inside the seacock easier. Red is lithium also (should be) if it's waterproof but it probably a higher viscosity. It should work also, if that's what you already have in your grease gun.

That would probably create unintended consequences. First, the amount of heat to be applied would be considerable because the heat would dissipate in the water. Second, enough heat could damage the nylon seals in a ball-type valve (if that's what you have). Third, significant heat could soften the bedding compound possibly causing a water leak at the base. I'm with Capt J, exercise the things to loosen them up. Always be careful with the amount of force you apply to something that covers a large hole in the hull. In the event that the bonding system hasn't always been up to snuff, the bronze can be weakened by electrolytic action to the point where something important snaps off

No heat !! You're asking for real trouble !
There must be an older kid on the dock that's willing to go down there for a few bucks and give it a whirl.....
I like the grease idea that the others have mentioned. That's new to me also.
I snapped the handle off at the stud on mine two years ago flush with the seacock in the closed position in the fall had to haul out the following spring and cut the old one out in sections with a Sawzall and install a new one...