Ah, but there are different kinds of infrared, it's a very wide spectrum of electromagnetic energy after all. It ranges from about 700 nanometers (0.7 microns) at the visible end to about 1 mm (1000 microns) at the microwave end. Wien's law states that the energy peak of blackbody radiation is at a wavelength in microns given by lambda(max) = 2900/T where T is the absolute temperature of the radiator in kelvins. So your M dwarf at 3000 K is going to radiate most strongly at around one micron, and CO2 is still quite transparent to that (see http://en.wikipedia.org/wiki/File:Atmospheric_Transmission.png for the CO2 absorption spectrum). CO2 is most absorbing in a wide band at around 17 microns, corresponding to a temperature of about 170 K.
Note that this is a better match for temperatures in the Arctic and Antarctic, where average temperature is around 240 K, compared to the tropics where average temperature is around 300 K, and global warming is definitely stronger in the arctic than in the tropics. But at some point, you can't describe such complicated physics in general terms like we are doing here, you need to do the detailed computer modelling.
On Venus, the atmosphere is so thick with CO2 that it is essentially opaque at all long infrared wavelengths and Venus has had to keep warming up until it could radiate out at shorter wavelengths and temperatures near 700 K.
At high altitudes on Venus, the CO2 becomes a much more efficient radiator than absorber, so it gets very cold. Again, the physics is complicated since the atmosphere is rarified enough to be in a state of non-thermodynamic equilibrium.