In the future I suggest you put copyable code into your posts to make it easier to help you, otherwise I needed to manually type it in.
inf->Infinity is the issue
pde=a D[temp[x,t],{x,2}]-D[temp[x,t],t]==0;
DSolve[{
pde,
temp[0,t]==0,
temp[Infinity,t]==0,
temp[x,0]==0,
(D[temp[x,t],t]/.t->0)==0
},temp[x,t],{x,t}]