I was thinking to use two Peltier element, one as heating unit and the other as cooling (to be sure that the temperature is really lower than 25 °C.
If you reverse connections (with an H-Bridge or a DPDT relay) you'll reverse the hot & cold sides of the Peltier. If you use a relay, you'll need a 2nd relay to turn the thing on/off.
But, a resistor is a "natural" 100% efficient heater so it may be a better solution for heating.
The gradient must be applied inside a device filled with very little amount of water. The length of the channel, where the water is going to flow, is 5-6 cm.
You can calculate the amount of energy it takes to increase a given volume of water by a given number of degrees.* But, since you don't have perfect insulation, the amount of energy loss is unknown. (I don't know anything about the efficiency of Peltier devices.)
So, you might want to start by experimenting with a resistor-heater. Once you know the amount of energy you need, you'll have a better idea of your Peltier power requirements.
- Of course, the same amount of energy must be removed to cool by the same amount.