Yeh that's right but be very careful not to over heat the slide it will warp. Are you sure it doesn't have a ding in it or it's not bent. Once you get it loose you can clean it LIGHTLY with steal wool just to get the green crusty crud off of it. Better to take it to the shop than to cause any damage. They probably won't charge more than 20 bucks to fix.
I just bought a used Yamaha trumpet to play taps at military funerals. The tuning slide was stuck . . . I took it to a local music store and they pulled it for $20. I wouldn't try it yourself, you'd probably bend or dent it and just make it worse. Leave it to the professionals.