In this paper, we report on a capillary microfluidic device with constant flow rate and temperature-triggered stop valve function. It contains a PDMS channel that was grafted by a thermo-responsive polymer poly(N-isopropylacrylamide) (PNIPAm). The channel exhibits a constant capillary filling speed. By locally increasing the temperature in the channel from 20 °C to 37 °C using a microfabricated heater, a change of the surface wettability from hydrophilic to hydrophobic is obtained creating a hydrophobic stop valve. The valve can be reopened by lowering the temperature. The device is simple to fabricate and can be used as an actuatable capillary pump operating around room temperature. To understand the constant capillary filling speed, we performed contact angle measurements, in which we found slow wetting kinetics of PNIPAm-g-PDMS surfaces at temperatures below the lower critical solution temperature (LCST) of PNIPAm and fast wetting kinetics above the LCST. We interpret this as the result of the diffusive hydration process of PNIPAm below the LCST and the absence of hydration on the hydrophobic PNIPAm thin layer above the LCST.