The observation that the thermometer reading on the sample holder increases when the Keithley 6221 current source is connected suggests that high-frequency noise from the current source might be causing the sample holder to heat up. Here are some suggestions and considerations to help diagnose and possibly mitigate the issue:

### 1. **Verify the Noise Filtering:**

- The existing low-pass filter with a cutoff frequency of 36 kHz might not be sufficient to eliminate all high-frequency noise from the Keithley 6221. You could consider using a filter with a lower cutoff frequency. Increasing the resistance (R) and capacitance (C) values to reduce the cutoff frequency could help in filtering out more of the high-frequency components that could be causing the heating.

### 2. **Use a Pi-Filter Configuration:**

- A Pi-filter (a combination of two capacitors and one resistor or inductor) could be more effective in suppressing high-frequency noise. This would provide better attenuation of noise and might help reduce heating.

### 3. **Check Ground Loops and Shielding:**

- Even though grounding has been completed, ground loops can still exist and cause noise problems. Ensure that all grounds are at the same potential and check for any possible ground loops. Use proper shielding and twisted-pair cables to minimize electromagnetic interference (EMI) pickup.

### 4. **Evaluate the Current Source Output:**

- Use a spectrum analyzer or an oscilloscope with sufficient bandwidth to directly measure the output of the Keithley 6221. This can help you identify any high-frequency components or oscillations that might be present. If high-frequency noise is detected, adding more aggressive filtering at the output of the current source may be necessary.

### 5. **Use a Low-Noise Power Supply:**

- Ensure that the power supply feeding the Keithley 6221 is low-noise and stable. Noise on the power line can propagate through the current source and cause unintended heating.

### 6. **Thermal Anchoring of Wires:**

- Ensure that the wires leading to the sample holder are thermally anchored at several points to minimize heat conduction. Even low levels of noise-induced current can cause heating, especially in low-temperature setups where thermal conductivity is a concern.

### 7. **Consider Alternative Measurement Methods:**

- If high-frequency noise remains an issue, consider using other methods for measuring electrical properties that might be less susceptible to noise, such as lock-in amplifiers, which can improve signal-to-noise ratio by focusing on a specific frequency band.

### 8. **Isolation Transformer or Ferrite Beads:**

- Place an isolation transformer or ferrite beads in the circuit to suppress high-frequency noise. These components can help block or attenuate noise that may be coupling into your system.

### 9. **Keithley 6221 Firmware and Settings:**

- Ensure that the Keithley 6221 is operating with the latest firmware version, as updates sometimes include improvements to noise performance. Also, check the settings for any options to minimize noise or enable output filtering directly on the Keithley device.

### 10. **Test with Different Current Ranges and Sources:**

- Try using different current ranges on the Keithley 6221 to see if the noise and associated heating change. Testing with an alternative low-noise current source could help isolate whether the issue is specific to the Keithley 6221.

By taking these steps, you can identify whether high-frequency noise from the Keithley 6221 is indeed causing the heating and find ways to minimize its impact on your low-temperature measurements.

Thank you Ranjith R. very much for your detailed explanation. I will check every point you mentioned.