# Is temperature discrete

Because an object's temperature is inversely proportional to the wavelength of blackbody radiation which it emits, physicists have theorized the existence of Planck temperature at around $1.4×10^{32}$ K.

Does this imply that temperature must be discrete? Meaning, the temperature could never be $1.0×10^{32}$ K, because that would imply a wavelength which is a non-integral multiple of the Planck length.

If it does imply this, does that mean that a system, if approaching the Planck temperature, and given more energy, would suddenly and radically change states from $0.7×10^{32}$ K to $1.4×10^{32}$ K? (perhaps much like a Bose Einstein condensate)

Pardon me if this question is bizarre, as I am not a physicist by profession (except maybe of the armchair variety).

$$T=\frac{m\overline{v^2}}{3 k_B},$$
The Planck temperature is an estimate maximum attainable temperature with the physics we know, to be attained by matter given the constants we know, and has nothing to do with discreteness as normal temperatures are around $300\text{K}$.