Automotive Sensor - Excessive Ripple Noise
Increase R5 and R10 to 50K and add a 1uF ceramic from U3 +input to ground and from U2 +input to a solid analog ground (keep the analog grounds together). Split R8 into two series 50K and add a 1uF ceramic capacitor to ground from the mid point. Lose the two Schottky diodes (too leaky, especially with 50K) and R11 (useless). 

Make sure your return wire from the RTD (you must have three wires running back to your circuit from the RTD, which must not be grounded at the chassis) is connected to the low side of R14 and thence to circuit ground as I said above about keeping them together. 

If you don't have access to a 'scope you'll be fairly limited, but if you're still seeing 'noise' try measuring the voltage at each op-amp output (including the current source) using a multimeter on the minimum AC volts range. Many will block the DC and show you some indication of what is going on in the AC world.