Will just an application of Reflectix help with the temperature gradient?
I would say there is a very good chance the Reflectix will more than enough. The best part about the stuff is that if you decide you want/need more insulation you can always pull it down, add foam-board and then put your Reflectix back up. I have moved mine more than once. Just put it up with foil tape and you can remove and re-use it.
If I have one concern with Reflectix only, or even the use of the double-sided foil faced stuff, it's that it might make the outside of the metal shed dangerously hot. If this is the case then a 2" layer of foam board (without a foil face) might be a good idea. And then Reflectix over that. This contradicts my previous post, but I had some time to reflect on what I wrote (sorry, no pun intended).
Insulation is a tricky thing and what works in one part of the country may not work in another.
Now, for a bit of personal experience, I live in the Black Hills of South Dakota and had a temporary snake room in the back of my previous garage. It was standard 2x4 construction with OSB and siding on the outside and drywall on the inside. No insulation in the walls or concrete floor. There was a small amount of blown in insulation in the attic above the room. Two of the walls were exterior, two were interior to the unheated garage.
I lined the walls, ceiling and hollow core door with Reflectix. I did not insulation the slab floor. The room was heated with a stand oil filled radiator style heater.
During that winter even when temps inside the garage were below freezing and outside temps were even colder than that, I was able to heat the room into the low 80's with that heater set on its lowest setting, I think 700 watts. The room was 7x7x8.
Far from ideal but it got me through that one winter easily.
If you use the stuff, make sure to apply it loosely so there is a bit of an air space behind it. And if there is some sort of built in insulation built into the shed, like in the eaves, make sure the Reflectix does not prevent air flow in these areas.
The more I think about it, the Reflectix is a great place to start. If in the future you want to do more, then line the inside with 2" thick foam board without a foil face. For even more protection, get one of the paintable radiant barriers and paint the outside of the shed.
One other comment, I only mention Reflectix because it's readily available and what I used. I assume all of the similar insulation products perform well.
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Currently keeping:
6.10 Gonyosoma oxycephala (Javan, mixed colors)
1.1 Philodryas baroni
1.0 Rhodesian Ridgeback