If it was hot it wasn't a genturi!!! I've seen folks just extend the generator exhaust with plastic pipe. Once I saw that type extension on a bus conversion -- several hours later there was a pile of melted pipe on the ground.
For the genturi to work the smaller exhaust pipe has to be surrounded with a 3-4" plastic pipe centered on it. As the hot exhaust rises it pulls cooler ambient air into the pipe and if working properly the combined air will be cool enough that the plastic pipe is barely warm at about 4 feet up. I made my own 15 years ago for about $10.
Parts list: 90 degree metal electrical conduit of proper inside diameter to fit the generator exhaust.
1 10foot 3" lightweight drain pipe (may need two)
2 4" small diameter bolts
drill a hole in the metal conduit for one of the bolts at the point where the bend ends and a second hole 90 degrees off near the end so the bolts form a cross. Matching holes in the drain pipe complete the construction. I cut my pipe into two 5 foot sections for ease of handling. Drain pipe has one end expanded so a coupler won't be needed.