It's hard to know exactly what happened to Laika. According to this abstract, the telemetry system failed on the 4th orbit, meaning the Soviets weren't receiving any signals from the spacecraft showing Laika's status. The telemetry information was only transmitted during a 15-minute period of each orbit, so there was no continuous monitoring of Laika, making it impossible to say exactly what happened.

We do know that Laika survived the launch, had settled back down from the stress of the launch, and was eating. However, because Khrushchev wanted a space launch to mark the 40th anniversary of the revolution, there was only one month to design Sputnik 2, and that short timeline did not allow for any testing of the environmental controls. The capsule overheated, and the Soviets decades later acknowledged that they believed that Laika died due to overheating sometime on the third or fourth orbit.