If the water temperature fluctuates while the water is running there are a few possible issues.
Check for cross plumbing between cold water lines and hot water lines. To do this turn off the cold water supply and turn on a hot water fixture. The water at the fixture should eventually completely stop flowing. If water continues to run you have crossed plumbing and should contact a plumber.
The filter on cold water inlet should be clean; look for signs of hard water scaling. If found Refer to your installation manual for descaling procedures.
On well systems or even on some city water systems, water pressure fluctuations (especially on low flow) of 8 to 10 psi will result in flow rate fluctuations, which will in turn result in minor temperature fluctuations.
There could be an issue your gas supply or venting. Contact a certified HVAC technician.