My first impression is that your two desires conflict with each other. 1) maximum temperature difference between light/dark sides and 2) gradual temperature change across a side. You may need to decide which is more important.
There can be a temperature gradient, yes, but I'm assuming it would be small enough that you don't get the effect you're looking for.
If you're ok with the gradient being just barely enough to accommodate the characteristics you want, maybe you can choose the parameters to be right on the edge of what you need. Want dry ice but not nearby? Say the night side is just a little too warm near terminator and just cold enough far away. It's not a large gradient, but it is just enough so you can have one thing nearby and a separate thing farther away.
There could also be other methods of getting what you want. At the furthest reaches of the light side, maybe there is a mountain range which has a lot of some reflective material, so nearby the mountains there is a spot where the reflected light is collected that is heated even more than the rest of the light side.
Now you have several levels of hot areas:
Near the light/dark terminator it quickly reaches hundreds of degrees. During their industrial revolution people managed to protect themselves from the heat long enough to set up conveyers and pipes which direct hot air back or which take objects out far enough to ignite before bringing them back. Imagine if all you had to do to start a fire was place your wood on a conveyer then crank a shaft to make it go out, catch fire, reverse to make it come back. Or to heat your home all you have to do is use fans to suck in the endless supply of hot air.
On the cold side of this they get free food preservation and air conditioning. Ducts and conveyers again.
Since they are piping in hot and cold air don't stop at the terminator; take it to the opposite side. Use the cold air to help you explore further into the hot area and the other way too.
Now they can go further out and they find lakes of liquid tin and lead. It was already hundreds of degrees nearby, it only needs to get a little hotter for these elements to melt. Though, with the lower air pressure you might have to maintain a better temperature gradient, the melting/boiling points may change.
They'll have to advance quite a bit more to explore the area near the reflective mountains. You can make that area almost as hot as you want. Just say the mountains are arranged in a circle and so much energy is concentrated at the center that you get into areas of liquid copper or iron, or where glass forms.
You can use your idea to get some of what you want, then with a few more creative ideas you can get more of what you're looking for.