This comes from the data sheet. I think you need a capacitor across the 15V close to the regulator. 1.5m is a long distance. The data sheet might be confusing so 'any cap is better than no cap'.
40C is fine.
You might have a grounding problem (ground loop). If the input cap makes no difference then we should look at your grounds. Can you send a picture?
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EXTERNAL CAPACITORS
An input bypass capacitor is recommended. A 0.1 μF disc or 1 μF solid tantalum on the input is suitable input
bypassing for almost all applications. The device is more sensitive to the absence of input bypassiing when
adjustment or output capacitors are used but the above values will eliminate the possiblity of problems.
The adjustment terminal can be bypassed to ground on the LM138 to improve ripple rejection. This bypass
capacitor prevents ripple from being amplified as the output voltage is increased. With a 10 μF bypass capacitor
75 dB ripple rejection is obtainable at any output level. Increases over 20 μF do not appreciably improve the
ripple rejection at frequencies above 120 Hz. If the bypass capacitor is used, it is sometimes necessary to
include protection diodes to prevent the capacitor from discharging through internal low current paths and
damaging the device.
In general, the best type of capacitors to use are solid tantalum. Solid tantalum capacitors have low impedance
even at high frequencies. Depending upon capacitor construction, it takes about 25 μF in aluminum electrolytic to
equal 1 μF solid tantalum at high frequencies. Ceramic capacitors are also good at high frequencies; but some
types have a large decrease in capacitance at frequencies around 0.5 MHz. For this reason, 0.01 μF disc may
seem to work better than a 0.1 μF disc as a bypass.
Although the LM138 is stable with no output capacitors, like any feedback circuit, certain values of external
capacitance can cause excessive ringing. This occurs with values between 500 pF and 5000 pF. A 1 μF solid
tantalum (or 25 μF aluminum electrolytic) on the output swamps this effect and insures stability.