A method and apparatus are provided for monitoring a parameter such as temperature in a system such as a computer server. The method involves defining a monitoring range for the parameter. Typically, the parameter initially lies within the monitoring range. The parameter is then tracked by determining whenever the parameter exceeds an upper or lower limit of the monitoring range. If such a limit is reached, the monitoring range is adjusted to try to accommodate the parameter within the adjusted monitoring range. A time history of the monitoring range may be recorded, including details of all the adjustments of the monitoring range. This allows the behavior of the parameter to be subsequently investigated for diagnostic purposes.