Re: Effects of a different CMBR temperature?
 

Well for terrestrial planets. It may matter for iceballs. It's much the same issue as the second stars of binary systems usually don't matter for the habitable planet's temperature.

Two temperature sources add as the fourth root of the sum of their fourth power. So if you have two sources that would heat something to 100K in isolation, their combination heats the thing to 119K, which could matter, but if you have a one source that heats it to 300K and add another that would heat it to 100K, the combination heats it to 300.9K, which is likely negligible.

Edit: Is there a goal here? If you want a setting where space happens to be warm, I wouldn't suggest tampering with cosmology. Look for an excuse to bathe the entire region of the setting in a hot gas cloud instead. Yeah it's a little tricky to justify why whatever heated a cloud light-years across didn't kill everything in the region, but you can probably come up with something. If another galaxy collided with the Milky Way you might be able to get a jet of gas getting tossed off in the direction of one of the Magellanic Clouds that would still be fairly warm when it got there with less handwaving than changing the expansion of the universe. Sure it'll pass through, or cool back down again in 10 or 100 million years, but your metaplot doesn't need that much time anyway, right?

Re: Effects of a different CMBR temperature?
 

30K may prevent the formation of planetary systems; 100K almost certainly will. Upper limit for having planets that support life is probably a CMBR temperature of 6-8K due to age of the universe effects. However, if somehow we teleport a planetary system into a location with a different CMBR, a 100K background would increase the temperature of a habitable planet by about 1.5 degrees kelvin.
If it's high enough it will cause increased background noise, but for the most part thermal emissions will be at wavelengths where the CMBR is dim. If your goal is to make detection in space harder, I wouldn't mess with the CMBR, just increase zodiacal dust by a lot. Or add an asteroid belt (blowing up Mars and/or Venus would accomplish both objectives).

Re: Effects of a different CMBR temperature?
 

I'm contemplating possible weird alternate universes or areas of weird physics, but decreased detection ranges are something that I consider a nice thing to look into at every opportunitly.

So speaking of such dust . . . how much can it be 'safely' increased, and how much of an effect can that produce on detection modifiers?

Re: Effects of a different CMBR temperature?
 

What's the physics of that? A lot of planets in our solar system seem to have formed where the blackbody temperature based on solar radiation is higher than either of those figures.

Re: Effects of a different CMBR temperature?
 

The temperature of a molecular cloud is one factor that inhibits collapse, which in turn prevents star formation. I haven't been able to find any firm numbers on this, though. However, if your cosmic background radiation is hot enough, it might prevent or at least slow down star formation.

Re: Effects of a different CMBR temperature?
 

It's based on Jeans instability, and works out to the minimum mass of a gas cloud that can collapse scaling with T^3/2. As such, a high temperature results in massive gas clouds collapsing into massive stars that burn themselves out in short order.

Re: Effects of a different CMBR temperature?
 

Oh, okay. Do we know the minimum mass in our universe, as a function of cosmic temperature back around 5,000,000,000 years BP?

Re: Effects of a different CMBR temperature?
 

Far as I can tell from brief research, not significantly different from now, gas clouds drop to around 10K and you have to go back 10+ billion years for the CMB to be hotter than that.

Re: Effects of a different CMBR temperature?
 

That's partially helpful, but I was looking for a lower limit on the mass of a stellar system, either in kg or in multiples of our sun's mass. If I have one lower limit and one temperature I can figure out other lower mass limits for other temperatures, but I need one starting point. Is there any estimate of how small a "star" could be at the time when our solar system was formed?

Re: Effects of a different CMBR temperature?
 

Ah, so we're talking about extreme values for the CMB temperature. That could probably be achieved by modifying the cosmological constants, i.e. tweaking the distributions of matter, radiation, and dark energy. A higher radiation density (for more energy) and a lower matter density (for less absorbing material at the big bang) might do the trick without radically altering things. At the moment the radiation energy density is negligible compared to the other constants, increasing it slightly shouldn't have much effect on the evolution of the universe (i.e. expansion and possible contraction).

From my understanding between 10K and 20K is the temperature when stars begin to form. So as Anthony said, you could probably get away with a CMB temperature of 6-8K before it increased the temperature of the clouds too much (the low temperatures are required for the clouds to reach sufficient densities). That's around triple what it currently is. Note however that because of the way temperature drops as the universe expands, an 8K CMB universe won't have been suitable for star formation for very long at all, even if it's a similar scale to our universe, in a lot of ways it'll look like our universe a long time in the past.