R, 150 144 141 bytes
a=scan(,"");U=c("C","K","F");i=which(U==a[2]);Z=273.15;x=scan(t=a[1]);cat(paste(c(C<-c(x,x-Z,5*(x-32)/9)[i],C+Z,32+C*9/5)[-i],U[-i]),sep="\n")
Indented, with new lines:
a=scan(,"")
U=c("C","K","F")
i=which(U==a[2])
Z=273.15
x=as.double(a[1])
cat(paste(c(C<-c(x,x-Z,5*(x-32)/9)[i],C+Z,32+C*9/5)[-i],
U[-i]),
sep="\n")
Usage:
> a=scan(,"");U=c("C","K","F");i=which(U==a[2]);Z=273.15;x=scan(t=a[1]);cat(paste(c(C<-c(x,x-Z,5*(x-32)/9)[i],C+Z,32+C*9/5)[-i],U[-i]),sep="\n")
1: 23 C
3:
Read 2 items
Read 1 item
296.15 K
73.4 F
> a=scan(,"");U=c("C","K","F");i=which(U==a[2]);Z=273.15;x=scan(t=a[1]);cat(paste(c(C<-c(x,x-Z,5*(x-32)/9)[i],C+Z,32+C*9/5)[-i],U[-i]),sep="\n")
1: 56.9999999 K
3:
Read 2 items
Read 1 item
-216.1500001 C
-357.07000018 F
> a=scan(,"");U=c("C","K","F");i=which(U==a[2]);Z=273.15;x=scan(t=a[1]);cat(paste(c(C<-c(x,x-Z,5*(x-32)/9)[i],C+Z,32+C*9/5)[-i],U[-i]),sep="\n")
1: 86.987 F
3:
Read 2 items
Read 1 item
30.5483333333333 C
303.698333333333 K
Thanks to @AlexA. & @MickyT. !