Check the Transmission Fluid first to make sure that its full. If the transmission is high mileage then it might need a filter and fluid change. If the Filter is ok then the transmission might need a rebuild.
700r4 is the stock transmission for all third gen camaros. the 700r4 is also known as the 4L60E
Are you sure that it's third it's not shifting into, and not fourth? The transmission is designed to not permit shifts into fourth (overdrive) until the engine and transmission have warmed up a bit.
A car with an automatic transmission shifts itself from 1st to 2nd to 3rd when you accelerate. You don't need to shift it...that's why they call it automatic.
the magna carta
The transmission may need a flush and filter, or in my 92 accord I solved the problem merely by changing the transmissions computer.
Your transmission's filter may be clogged, you may be low on transmission fluid, or the transmission may need repair or replacement. If the transmission was full of fluid, I would suggest a transmission flush, or replacing the transmission filter and fluid. If this doesn't help the transmission may actually be damaged and may need repair or replacement.
In automatic transmissions the second to third syncronizers always seem to go bad first, the syncronizers are worn, bad or gone. This is common in these transmissions. Also you might check your trans fluid level, sometimes a low level will cause the transmission not to shift correctly.
Ford offered two transmissions that year. A 5-speed manual transmission was standard with the 2.3-liter, four-cylinder engine as well as with the 2.9-liter, V-6 engine. A 4-speed automatic was optional. A third engine, a 4.0-liter, V-6 offered the 4-speed automatic transmission only.
It wants to go to third and fourth gear as the road speed increases so as to allow the engine to run at a more optimum speed.
Automatic transmissions work on a combination of fluid pressures and electronic signals. Make sure the fluid level is proper, and does not smell burnt. Burnt fluid can be a signal that discs are slipping in the transmission. Also check to see that the linkage is tight and set properly. An unadjusted linkage can cause the transmission to not go into the proper gear.
If it vibrates briefly only while shifting, it's probably the transmission slipping. If all other gears are shifting ok, you're about to loose the transmission.
Check your tranny fluid. If it's full, you need to get your transmission checked. The screen could be dirty and need to be replaced, or the transmission itself could need to be repaired/replaced.