The datasheet gives some strong advice on decoupling.
Note the 0.1 µF bypass capacitor on the input. This capacitor
should be a ceramic type, have very short leads (surface-mount
is preferable), and be located as close as possible in physical
proximity to the temperature sensor supply pin. Because these
temperature sensors operate on very little supply current and
may be exposed to very hostile electrical environments, it is
important to minimize the effects of radio frequency interference
(RFI) on these devices. The effect of RFI on these temperature
sensors specifically and on analog ICs in general is manifested as
abnormal dc shifts in the output voltage due to the rectification
of the high frequency ambient noise by the IC. When the
devices are operated in the presence of high frequency radiated
or conducted noise, a large value tantalum capacitor (±2.2 µF)
placed across the 0.1 µF ceramic capacitor may offer additional
Did you comply?
The datasheet continues ...
Figure 32 illustrates a way to convert the output voltage of a
TMP35/TMP36/TMP37 sensor into a current to be transmitted
down a long twisted pair shielded cable to a ground referenced
receiver. The temperature sensors are not capable of high output
current operation; thus, a standard PNP transistor is used to
boost the output current drive of the circuit. As shown in the
table in Figure 32, the values of R2 and R3 were chosen to
produce an arbitrary full-scale output current of 2 mA. Lower
values for the full-scale current are not recommended. The
minimum-scale output current produced by the circuit could be
contaminated by ambient magnetic fields operating in the near
vicinity of the circuit/cable pair. Because the circuit uses an
external transistor, the minimum recommended operating
voltage for this circuit is 5 V. To minimize the effects of EMI (or
RFI), both the circuit and the temperature sensor supply pins
are bypassed with good quality ceramic capacitors.
See also the 4-20 mA section.