I'd allow it, but it'd be very slow. You're using a 2nd level spell slot for 1 minute of heat. You can get some work done in that time, but not much, especially on good steel. In addition, you'd still be expected to have smithing tools (hammer, tongs, gloves, etc.), an anvil, materials for proper quenching, possibly a grinding wheel, etc, if you want to forge a quality weapon.
It's imaginative, so I'd want to reward that, but the idea of having heat available for only a few minutes a day would slow any real work down to a crawl.
Edit: In a survival situation with limited supplies, it might be worthwhile, but I wouldn't make it a super-amazing, better-than-a-real-forge option.