Some trains from Glasgow Central - the country's busiest station - were suspended for a second evening after temperatures in the city hit a record 31.9C.
ScotRail said: "Due to high rail temperatures, we’re having to reduce services to and from Glasgow Central High Level.
"Those that are running will be subject to delay and alteration."
Trains were also halted between Edinburgh and Bathgate after rail temperatures reached 51C at Livingston North station.
Services on the main Edinburgh-Glasgow line were halved to half hourly because of similar problems near Edinburgh Park.
That also forced trains between Edinburgh and Dunblane to be halved to hourly.
There were also cancellations on the Glasgow-Lanark line, where services were halved to hourly.
Rail staff handed out water to passengers at Central and Queen Street stations in Glasgow as the city hit a record high of 31.8C.
But others vented their fury on social media as they sweltered on delayed trains.
Physio Jill Adams tweeted: "Trying to get to Livingston on the 16.03. It’s on/ off/ on again meanwhile waiting in a packed, inhumanely hot train. Where’s the air con?"
Some complained of "chaos" at Queen Street and Central, and lack of information.
Jessica tweeted: "I’m currently away to collapse in queen street cause it’s a greenhouse and every single train is delayed. It’s mayhem."
Some commuters passengers questioned why the rails couldn't cope with high temperatures, unlike hotter countries.
But Network Rail said because of our variable weather it was neither practical nor cost effective to stress rails to cope, as happened in other countries, and this could put them at grater risk in the winter.
Speed restrictions were also being imposed on other lines to reduce the risk of tracks buckling.
They included at East Linton on the Edinburgh-London east coast main line in East Lothian, Newbridge in western Edinburgh, Inverkeithing in Fife, and Helmsdale in Sutherland.
Network Rail said rail temperatures reached 39C near East Linton.
On the Lanark line, ScotRail said 13 services would not run or have their journeys curtailed this afternoon.
That will cut direct trains by half to hourly, including during the afternoon rush hour.
Further delays were caused by signalling faults between at Holytown and between Uddingston and Cambuslang in South Lanarkshire, which affected trains on a secondary Edinburgh-Glasgow lie via Shotts.
Glasgow-East Kilbride were services disrupted this morning by a cow on the line between Hairmyres and East Kilbride.
The disruption follows all trains being halted at Glasgow Central - Scotland's busiest station - last night after several sets of points between tracks expanded in the heat and stopped working.
Engineers have painted rails white at the station in an attempt to avert a repeat of the disruption.
Network Rail said this meant they absorbed less heat and expanded less.
Temperatures reached 31C in Glasgow today after hitting 28C yesterday.
Speed restrictions are imposed during high temperatures to reduce the risk of rails buckling.
This means trains take longer to complete journeys and reduces capacity, such as on single-track sections of lines.
A ScotRail spokesperson said: “We sincerely apologise to customers affected by this disruption and completely understand their frustration when these things happen.
“Customers can get the latest service information on social media, on our website and mobile app.
“Anyone delayed by 30 minutes or more is entitled to compensation under our Delay Repay guarantee.
"To claim, simply keep hold of your ticket and visit our website or mobile app.”
A Network Rail spokesperson said: “Last night’s problems were caused by a fault with with the air-driven points equipment which moves the rails to switch trains between one track and another at the junctions outside Central.
“A drop in air pressure due to a loose air hose caused the equipment to fail and the exact cause of this fault is still under investigation.
"With record breaking hot weather predicted in Scotland, Network Rail has activated its extreme weather action team to ensure passengers are kept safe and our railway keeps running as reliably as possible."
David Dickson, Network Rail’s infrastructure director for the ScotRail Alliance said: “On very sunny days, rails in direct sunshine can be as much as 20 degrees centigrade above air temperature causing the steel to expand markedly and could, if not carefully monitored and action taken, buckle causing travel disruption.
“Our engineers and specialist extreme weather teams are monitoring track-side temperatures and vulnerable locations and will, if necessary, introduce temporary speed restrictions during the hottest part of the day to keep trains running, albeit more slowly than normal.”