I think it will probably be okay, based on what you've told me.

It is sometimes quite difficult to assess a baby's temperature based on feel, especially as it is not uncommon for them to have warm or cool extremities. The best way to feel is to feel their chest or back. Ear thermometers are also quite hard to use accurately at this age.

I would check their temperature again when they wake up, and throw another blanket on in the mean-time, as long as they are otherwise well. If he develops any other problems - vomiting, a rash, fevers, shivering or chills, difficulty breathing - then get him checked out. But at the moment, it sounds like he was just grumpy this morning after his immunisations and has settled down a bit now.