I would add a cardigan to the vest and baby grow in the day time. I would say no to a hat indoors at that temperature.
For night time, I found the gro egg, sleeping bags in various togs and the little dressing guide that comes with the gro egg incredibly helpful. It’s a chart of what layers are recommended depending on the temperature, and it takes the guess work out of dressing the baby - especially for stressed first time parents. Link to the guide here - scroll all the way to the bottom of the page:
www.tommeetippee.com/en-gb/discover/sleepwear-range
Personally I didn’t like to use blankets in the cot, even as a now parent of three. I don’t like the potential of the blanket to shift. But of course if you’re happy with that, do carry on - but a cellular blanket is recommended to reduce risk of suffocation.
I would agree that a thermometer is not really necessary unless you suspect a fever. Their chests and backs are supposed to be relatively lukewarm, rather than hot. Hot would indicate overheating or a temperature.
For thermometers, we have a digital underarm for the newborn stage, when their ear canals are too small to use an ear thermometer accurately. We then used digital ear thermometers from around 6 months.
But again- I wouldn’t use one unless I suspected a temperature. I’m sure you know this, but any temperature over 38C is an A&E situation for a baby under 3 months. It’s not even worth trying the GP first, because they will send you straight to A&E. But hopefully you won’t experience that anyway.