Depends on how the engine is rated for max thrust. Most modern engines are "flat rated" to a designated temperature, often around 30 deg C, so to get the rated thrust you need more N1 as the temperature increases. Flat rating can also include an altitude range, so as altitude increases you need more N1 to achieve the rated thrust.
However, many airline take-offs are made with reduced thrust, called "derate" or "Flex" by different manufacturers, so you are not then using the full rated thrust -it's kinder to the engines and lengthens their life.