If i woke at 3am and baby felt hot, and unwell i would give panadol or take to the drs regardless of temp is what i mean.

But yes for piece of mind if you are just checking to see if the temp is over 38 degrees a basic thermometer you can slip under their arm is fine for a newborn, the more expensive tympanic thermometersare often too big of the ear canal of a newborn and will give an inaccurate reading.
Just pop under the arm and hold bub close to you with that arm tight aginst your body so bub cant move it

If you want to go down the track of a tympanic for the older years due to time contraints you can but if your child is sprouting a high temp he or she will usually be unwell enough to be still for 1 minute to use a basic digital one too