will there be any change in pH value of neutral water if temperature is changed ? what will be the the room temperature if the pH value of water in 6.5 ?

The formation of hydrogen ions (hydroxonium ions) and hydroxide ions from water is an endothermic process. Using the simpler version of the equilibrium:
H2O(l)⇌H+(aq)+OH−(aq)
Hence, the forward reaction, as written, absorbs heat.
T (°C) Kw (mol2 dm-6) pH
0 0.114 x 10-14 7.47
10 0.293 x 10-14 7.27
20 0.681 x 10-14 7.08
25 1.008 x 10-14 7.00
30 1.471 x 10-14 6.92
40 2.916 x 10-14 6.77
50 5.476 x 10-14 6.63
100 51.3 x 10-14 6.14
from the table at pH=6.5 temperatur would be around 50-6 degree celsius