Yes, you can run your dishwasher using hot water only. Most dishwashers are designed to accommodate both hot and cold water supplies, but they have built-in heating elements to heat the water if it is not hot enough. Running the dishwasher with hot water only will not cause any damage or issues.
However, keep in mind that if your dishwasher relies solely on hot water, it may take longer for the dishwasher to complete its cycle as it needs to heat the water internally. Additionally, using hot water only may increase energy consumption compared to using a combination of hot and cold water.
If the cold water feed to your kitchen is being worked on, running your dishwasher with hot water only is a suitable temporary solution. Once the cold water supply is restored, you can resume using the dishwasher as usual.