There are two ways to transfer heat: convection and radiation. Convection is what you get when you touch something hot, radiation is when high energy photons touch you.
Since there's not a lot of things to touch in space, convection is basically right out. Sure you get some high energy plasma fields and so on, but generally there's not a lot of matter hanging out in the vaccuum... by definition, really. In space what really matters is radiative heating/cooling.
A body with a lot of thermal energy is constantly emitting photons in the infrared band, and each one of those photons carries away a small amount of the thermal energy. Over time the body cools to the lowest possible level due to radiative cooling. At the same time you're receiving photons from everything you can see. Those photons that are absorbed add their meagre energy to your body, exciting your electrons and warming you up. Those excited electrons eventually settle back down and emit photons again.
The equilibrium point, where you are receiving as much as you are emitting is what we often refer to as the temperature of space. In deep space, far from any pesky radiation sources, you're still awash in remnant photons from the microwave background. Leftover energy packets from the pre-expansion universe are still kicking around, and an ideal radiator will still receive enough of them to keep its temperature above absolute zero. Not by much though.
But that's the "real" universe, to the best of my knowledge at least. In your divinely created young universe the rules are clearly different. It's small enough that any reasonable collection of remnant photons would be absorbed fairly quickly, so it won't have a lot of longevity. The ones that aren't quickly absorbed will likely wander off on paths that take them out of the local space and be effectively lost forever.
Unless they have a reason to turn back.
The simplest solution would be a perfect black-body envelope with only one side. If the entire universe is enclosed in a shell of perfectly absorbtive material that radiates energy back into the universe at the same rate then you can maintain an enclosed system at any temperature you like. Objects in space would then be heated fairly evenly from all directions, and any heat they lose would eventually return to them.
Of course now you have the problem that the entire universe will settle into thermal equilibrium pretty quickly. With everything at the same temperature it's hard to get any work done from it. You'd need some way to produce variations in the temperature to get this to work.
One option would be to have significant anisotrophy in the envelope. Instead of releasing energy uniformly the shell could have specific areas that absorb the heat and other areas that emit heat back into the system. This would give you temperature gradients across the enclosed volume, allowing work to be done between areas of differing temperature. Objects in space would have a hot side and a cold side, etc. You could even have the shell emit from different areas in a cycle, vary the emission temperatures and so on. All in IR photons, of course. No lights in the sky, just patches of warm and cold.
Might be quite a pretty sight once you develop IR cameras. But I digress.
Physics in our own universe wouldn't allow a truly closed system like this to exist, but we're talking about a micro-verse created by gods with access to literal miracles. I'm sure they can whip up some perfect perfect heat transfer materials in no time. Or just... make it work by magic. That seems to be the way most godly stuff happens.