My puppy is 11 week old and just had her first injections this week. Today she has a bit of a runny nose and is a little lathargic and doesn't seem to be interested. She is eating well and drinking well and her poops are solid.
All in all she doesn't seem herself though. My husband took her temperature and it read 40c I don't know the normal range for a puppy.

If I am calculating correctly 40 celsius is 104 fahrenheit which is a little high.
A normal temp for a dog is about 101-102 fahrenheit.
So your pup does have a fever which will in turn make him not feel well.
It is normal for a pup to be a little under the weather after vaccines but they should be back to normal in about 24 hours, depending on when the vaccines were given I would give the vet a call and let them know about this.