[paul.fr]

lets say for general house plants, will room temerature water or slighly hotter warmer lead to better growth or does it not matter?

[dentstudent]

For house plants, ambient temperature water is the best to ensure that no sort of system shock occurs in the fine root system. Most of the nutrient exchange processes occur in the fine-root system as it has the higher surface area to volume ratio. Any damage to this through sudden environmental changes will potentially reduce a plants vigour, whether its a house plant or not. The temperature variability of the water is generally  less critical in outdoor plants as they are in much deeper soils, and the water has time to warm/cool as it percolates through the soil.