My understanding, which is not all encompassing, is that tankless water heaters generally have a specified range of water flow rates they can properly heat. Below a minimum water flow rate the water heater cycles much too quickly as a very short duration of heat energy rapidly raises the water temperature since the arrival of fresh cold water is happening slowly.

Often a tankless heater will have a minimum flow sensor and will not heat the water at all if the flow rate is too slow.

Some tankless heaters may have a special heat/power management system that allows them to heat water despite rather slow water flows without excessive cycling of the heat source.

At the other extreme, if the end device (one or six shower heads, bathtub filler, or whatever) is flowing a ridiculous (from the tankless water heater's perspective) amount of water per second, then even at full tilt the heater just cannot get the passing water up to target temperature before the water has flowed out of the heater and heads towards the naked user

The hot water consuming device is the determinant of water flow rate through the tankless water heater. If the heater cannot keep up, the water just comes out cooler than desired. Slow the water flow rate down (turn the tap for less flow) and the water temperature coming out of the tankless heater will rise.

As long as the water flow rate through the tankless heater is between the manufacturer's specified upper and lower flow rates, the water temperature coming out should be at or close to the set temperature.

I recall this being one of the primary early complaints with tankless water heaters. The 'hot' water temperature would fluctuate. Slow the kitchen faucet down to a trickle and the water would become cold, increase the tap flow just enough and the heat would return. Run the water too fast and the temperature could decrease.

I expect the better designed tankless heaters can now cope with a fairly broad range of water flow rates, but at the extremes the phenomena can still occur.

There are interesting options such as using a parallel compact storage tank (with or without its own heating element) to accumulate hot water from the tankless heater, allowing the tankless burner to run for a more reasonable time period instead of rapid cycling, and also provide a source of accumulated hot water when the flow rate is very slow. Sometimes a small circulation pump is used to keep the storage tank temperature close to optimum and reheat the water as needed during non-use periods.

Part of the specification for a tankless water heater is the maximum temperature rise that is possible for a given water flow rate. If the water entering the tankless heater is very cold, a greater temperature rise is required to deliver the target hot water temperature.

Put another way, the colder the supply water the slower the maximum water flow can be and still deliver the target water temp. If you turn the tap to flow more water per second that the heater can provide given the needed temperature rise, the heater will do its best and you will get undercooked hot water.