Some softbox specs have a wattage rating - the Fotodiox Pro stuff I have says 400 watts. Speedotron modeling lights are 250 w (102 head) and I've never had problems with any standard softbox. But for a hot light, you do want a purpose-made hot light box as Gorbas mentioned. You can often find them used on eBay, often with Photoflex Starlights, which are 500 and 1000w tungsten fixtures that work pretty well with their softboxes.
The thing about fresnels is they're already an inefficient light source and just blasting them onto a soft box face cut efficiency even more (softboxes are designed for a bare bulb to stick well into the box, allowing the reflective surfaces inside to help; open-faced lights fare a little better. The Starlights use a very long bulb that sticks way into the softbox). Fresnels are great for use without any other gear (other than barndoors), as they have a soft-but -directional look can look classic on a face and of course excels for back or rim or hair lights, or slashing light across a backdrop.
I do have a lot of rectangular open-faced lights, and I'll aim them at a frame with diffusion (a foot or more back so the diffusion doesn't discolor or melt). Controlling spill can mean rigging black fabric or cards around the whole thing, so it's much better for higher-key looks. Keep in mind that diffusing a tungsten light can really knock the output down.