It depends a bit on the receiver's quality, I've had experiences where the SNR could drop to about 8 and the link would still somewhat work.
The thermal noise is mostly intrinsic to how energy relates at a particle level, this is denoted by the Boltzmann constant (k). Further, it depends on the bandwidth (B) used and temperature (T). Nthermal = B * k * T = 20*10^6 Hz (802.11 channel) * 1.38065*10^-23 J/K * 300 K (27 Celsius) ~= 8.28 * 10^-11 This gives the noise in Watts, to change it to dBm (which references miliWatts), you take 10*log10( N * 1000 ) ~= -100. [1] Has a nice table with examples of this noise.
In reality, there's more interference than just from the temperature. It's quite probable your receiver adds another 5 dBm to its reported noise to account for this. I also recall from my time working on my thesis that receivers/drivers tend to return a static value for noise, rather than actually measure it.
[1]:http://en.wikipedia.org/wiki/Thermal_noise#Noise_power_in_decibels