Practical information about Wat Niwet Thammaprawat
This temple is not in Ayutthaya but in Bang Pa In.
No admission fee but donations to pay the cable car operating costs are welcome.
Reaching Bang Pa-In railway station takes between 1 hour and 1h45 from Bangkok depending on the trains (see Bangkok - Bang Pa In trains timetable)
or around 15 minutes from Ayutthaya (see Ayutthaya - Bang Pa In train schedule)
. Then right in front of the train station you will find either a collective taxi (songthaew) which will take you to Bang Pa-In Royal Palace
for 15 THB or a motorcycle taxi station (fare 20 THB). Otherwise this is only 20 minutes walk to go to the parking lot of the royal palace where the cable car to the temple strats.
I recommend that you combine visits to the royal palace and Wat Niwet Thammaprawat. It is done very well by train back and forth from Bangkok or Ayutthaya. You just have to locate the train schedules well knowing that you do not need to buy tickets in advance, at the station just before departure, that is enough and that allows a little flexibility on the return schedule. However, allow a minimum of 2 hours on site to visit the royal palace and an hour for the temple.