In an Adiabatic process, TVγ−1=‌ constant ⇒T1⋅V1γ−1=T2V2γ−1⇒T2=T1(
V1
V2
)γ−1 ‌‌ Here, ‌r=1.5,V2=V1∕2 ‌‌ and ‌T1=37∘C=310.15K ‌‌ So, final temperature is ‌T2=15×(2)1.5−1 =310.15×√2 =437.31K=164.12∘C ≃165.3∘C