somewhere in the last 30 years or so, my car became the recipient of a transmission cooler.  the lines from the radiator were taken off and then plugged on the radiator.

Like Ron said..."Under da FLOOR?!?!?"
Not good
Replace that cooler with one mounted up front, in front of the radiator-A/C condenser. The factory hard lines may still be there, so it will be a simple deal to do. If the hard lines are not still there, you will need to install new ones, and run them to the cooler ONLY, not thru the radiator.
This is a fairly simple operation, so most anyone can do it. If you have to replace the hard lines, you willl need to get it up in the air a bit, on jack-stands. You can buy new pre-formed lines from most 'Vette suppliers, but you won't be able to install them without bending the crap out of them. Since you're gonna have to bend them anyway, just go to your local parts house, and get two 6' sticks of 5/16" fuel line, and bend it to fit.

thanks for the info guys.

It is better to NOT run the trans cooler thru the rad. cooler. An auxillary cooler, mounted up front, will cool better. If you live in Terry-Land(Alaska!), you would benefit from running thru the rad.
In the trans business, we NEVER run the trans thru the radiator. Some may argue this, but, I've been doing it this way for 30+ years, and haven't had a cooler related failure yet.
The cooler can be mounted several ways. With strap metal/bolts, or with plastic ties that go thru the rad. core/cooler, to hold them together. If you purchase a new cooler, it will have these attatching peices, and instructions.

thank you, thank you.