The questions keep coming, to time to add more information.

"Heated the new ring gear with acetylene torch and it just would not stretch enough to fit over the flywheel. Because we heated the ring gear until it turned blue and then after several failed attempts to mount it on the flywheel, we allowed the ring gear to cool and walked away from the project, is it necessary to harden the ring gear before I pay the machine shop to mount it? Some suggestions as to how to go about hardening the ring gear, if necessary, will be greatly appreciated".

Blue or Dark Blue is okay and does not anneal the heat treated hardness of the ring gear. But it is not quite hot enough for sufficient thermal expansion of the ring gear. By the Book, it must be heated to 300-400dC (572-752dF) indicated by light blue surface color. Temperature above 750dC (medium red) will affect temper of the teeth.

If you are going by color to judge temperature,
410F = Light Yellow
430F = Straw Yellow
450F = Yellow
460F = Dark Yellow
480F = Yellow-Brown
500F = Red-Brown
520F = Purple
530F = Violet
550F = Dark Blue
570F = Blue
590F - Light Blue
610F= Gray-Blue
630F= Gray-Green
800F= Dark Gray
1000F= Very Slightly Red (mostly Gray)
1100F= Slight Red
1200F= Dull Red
1300F= Medium Red
1400F= Red
1500F= Bright Red

Temperature in the 1000F range is required for heating before quenching for hardening of the steel. Temperature in the 600F+ range is required for tempering of the steel after hardening. The tempering process does not destroy the hardness required for a gear, it only reduces if enough to make it less brittle (tougher). Tempering up to 750dF is acceptable for the ring gear.

If you over heat it for thermal expansion and it begins to turn red, then quench it with oil for proper cooling rate to restore hardness without making it too hard (or brittle). Pouring oil on red hot steel is a messy process you must be prepared for in advance. It will generate lots of smoke and stink, so doing it outdoors in a large metal tray is a good idea.

If you heat the ring gear to red then drop on the flywheel and allow it to air cool, it will be annealed (soft). Then you're screwed, because you cannot heat treat it when it is in assembly with the heavy flywheel without overheating the flywheel. You would have to cut the ring gear off and buy another one. With proper fixturing and a big enough press you might be able to press the flywheel out of the ring gear (or the ring gear off of the flywheel). If you do not destroy the ring gear during removal it could be heat treated and annealed again to restore hardness and toughness.

For the curious, coefficient of thermal expansion for steel is 0.00000633 per degree Fahrenheit. The ring gear is (nominally) 10.75" diameter. Heating the ring gear 500dF (from 90dF to 590dF minimum) will expand it 0.034" (1/32"). Pushing it all the way up to 750dF will add another 0.011" to the expansion.

For installation with the acetylene torch, use the largest flame tip available, and just keep heating the ring gear (evenly all the way around) until it drops on. You may need to get all the way to light blue or slightly beyond. Gray-Blue or Gray-Green is okay, but loosing most of the color going to Dark Gray should be avoided.