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I am trying to run a constant temperature MD calculation to see the effect of temperature. In my INCAR file, I have set TEBEG = TEEND. The MD runs relax to lower temperatures although TEEND is the same temperature as TEBEG.

I have coupled the system to Nose thermostat. My appreciations if some one could tell me how to get a constant - temperature result?

please check whether this drift in T might be due to the coupling to the thermostat (in case of doubt, it would be safest to set SMASS=0)

I did set SMASS=0, but it did not help. My system is an iron cluster of 13 atoms with icosahedral symmetry. It is surrounded by a vacuum region three times the size of the cluster. I am wandering if such a system consisting of two different components could be handled by a Nose thermostat.
My INCAR file looks as follows:
ISTART=0
ENCUT=300
ISPIN=2
MAGMOM=4 4 4 4 4 4 4 4 4 4 4 4 4
VOSKOWN=1
IALGO =48
WEIMIN = 0
#NELMDL=6
ISMEAR=1
SIGMA=0.2
AMIX=0.2
BMIX=0.0001
ANIX_MAG=0.8
BMIX_MAG=.0001
TEBEG=400
TEEND=400
LREAL=A
NELMIN=4
MAXMIX=50
ISYM=0
NSW=100
NBLOCK=1
KBLOCK=100
SMASS=0.0
POTIM=3.0

The linear charge mixing worked well for T=0; gave results that agreed with all-electron calculations. So I wanted to do the same calculation for finite temperature to see the effect of temperature.
My POSCAR file looks like:
1.0
16.0 0.0 0.0
0.0 16.0 0.0
0.0 0.0 16.0
13
Selective dynamics
Cartesian
-0.047166 -1.253482 -1.514631 T T T
0.052335 1.148221 -1.819558 T T T
-2.093502 0.145453 -1.217773 T T T
-2.086611 0.126754 1.236684 T T T
0.064268 1.122189 1.841974 T T T
-1.176674 2.016017 0.021025 T T T
1.353132 1.925775 0.012562 T T T
2.117561 -0.006829 -1.226835 T T T
-2.089440 -1.846959 -0.007182 T T T
-0.037637 -1.271156 1.494186 T T T
1.938155 -1.999076 -0.018546 T T T
2.127499 -0.024096 1.218931 T T T
-0.121911 -3.082812 -0.020825 T T T

The KPOINTS consits of GAMMA point. The 1998 POTCAR file for iron was used (The PAW One).