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The issue is that your timers are going out of scope and are destroyed. You need to make timerReadTemperature and timerPublishTemperature (private) class members.

class TemperatureSensor
{
public:
    TemperatureSensor(ros::NodeHandle *nh);
    double readTemperatureSensorData();
    void publishTemperature();

private:
    double temperature;
    ros::Publisher temperaturePublisher;
    ros::Timer timerReadTemperature;
};

and

TemperatureSensor::TemperatureSensor(ros::NodeHandle *nh)
{

    temperature = 0.0;
    temperaturePublisher =
            nh->advertise<std_msgs::Float64>("/temperature", 10);
    ROS_INFO("TempSensor Published.");

    timerReadTemperature =
            nh->createTimer(ros::Duration(1.0),
                    std::bind(&TemperatureSensor::readTemperatureSensorData, this));
    ROS_INFO("TempSensor Read timer started.");

    timerPublishTemperature =
            nh->createTimer(ros::Duration(1.0),
                    std::bind(&TemperatureSensor::publishTemperature, this));
    ROS_INFO("TempSensor Publish timer started.");
}