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LMT70: Need Faster Thermal Response Time

Part Number: LMT70
Other Parts Discussed in Thread: TMP103

The datasheet mentions that a response time of 1.3sec can be achieved in "stirred oil". How do I implement this into my design? Right now, I have the sensor on a PCB with a heating element placed on top of the sensor. I would like to sense the temperature of the heating element over time. If adding the oil isn't practical for my setup, then the LMT70 has a thermal response time of 73 degC. Can anyone recommend a temp sensor with faster response time (2 seconds) and sub-1 degree accuracy?

Thank you.