I would suffer third degree burns attempting to check the oil that soon. I had my Paragon rebuilt last year and the shop told me to start the engine, run for a minute, to ensure the oil cooler and hoses were filled, shutdown and check the oil. They indicated that it was most important to be on the full mark and not above or below.
The manual for Velvet Drive says the same thing, but adds that once you've checked and corrected it immediately after running you can let it sit overnight, then put a new mark on the stick at the "cold" level. You can then check it hot or cold. That should work on any brand.
Not familiar with Paragon but I would think if the oil gets hot enough to burn you, there's something wrong. My Velvet Drives run barely warm to the touch. Years ago a friend did get burned after the trans stopped working, he went down to check and it sprayed hot oil on him. But it had stopped working due to clutch slippage. I don't know what make it was.