Junkyard hood and throw a package of GM cooling system tablets into the thing. I'd bet it'll be fine.
I've had 4 different N* cars of all generations: '94 STS, '98 STS, '03 STS, and a '97 Aurora. I had literally ZERO issues, cooling system wise, with any of them. The Aurora was the worst offender, the front end design allowed for basically no airflow through the radiator unless the car was moving.
That car suffered badly from heat soak. I'd park it after an extended drive, run into a store quick, and upon start up be presented with an almost pegged temp gauge. It always made me nervous, but nothing came of it.