To answer the questions :
I think NR impose speed limits above a certain temperature? Is that right?
Kind of right. Speed restricitions for heat are usually only imposed in two circumstances :
1) for specific stretches of track where there is an increased risk of track buckles due to the condition and/or status of the track. These restrictions can be any distance, but typically less than a mile. They will be imposed when the
rail temperature reaches a certain level (that level will vary site to site due to the specific circumstance at that site), and occasionally may be imposed ahead of the time thst rail tempersture is reached on the solid expectation that it will be reached. The hotter the air temperature, the more sites will be affected.
2) for specific issues with certain types of (older) OLE equipment. Such restrctions are rare, and require very high air temps, but they can happen. These are usually imposed over much longer distances.
Sometimes, in very hot conditions, there can be a large number of speed restrictions, and therefore a ‘blanket’ speed is imposed over a wide area to reduce the number of restrictions being imposed / removed, as this then helps avoid confusion for drivers, and also reduces the number of people needed to put out and remove warning equipment, and the disruption that causes.
I'm guessing that might be likely later in the day.
Yes, more usually afternoon.
Does the amber heatwave warning trigger any preemptive action?
Yes, there have been (and will continue to be) specially arranged meetings / calls to co-ordinate additional response, control arrangements, communications channels, etc. These will consider all the places where there is potential for speed restrictions on a site by site basis, and also any intel on additional or unusual passenger demand on the days concerned.