Trouble in interpreting and calculating temperature effect of an amplifier module
Referring to your previous post titled A question about temperature change of a transducer, the load cell's sensitivity is defined as \$C_n=2\,mV/V\$, and the load cell's temperature effect on sensitivity \$TK_C\$ is specified as \$0.05\,\%\,of\,C_n/10\,K\$:

$$
C_n=C_{n0}+0.05\,\%\;C_{n0}\left ( \frac{T-T_0}{10} \right )
\;\;\;\;\;\;\;\;\;\;(1)
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\rightarrow
C_n=C_{n0}\, \left \{ 1 + \left ( \frac{1/20}{100} \right ) \left ( \frac{T-T_0}{10} \right ) \right \}
\;\;\;\;\;\;\;\;\;\;(2)
\\[0.35in]
\rightarrow
C_n = C_{n0} \left ( 1 + \frac{T-T_0}{20,000} \right )
\;\;\;\;\;\;\;\;\;\;(3)
$$

where

T0   = Load cell's initial (or reference) temperature, e.g., 25 °C
T    = Load cell's final temperature
Cn0  = Load cell's sensitivity when the load cell's temperature is T0
Cn   = Load cell's sensitivity when the load cell's temperature is T


The amplifier module's data sheet claims that for each 10K increase in ambient temperature, the amplifier affects the load cell's sensitivity1 by less than 0.1% of full scale, where "full scale" is \$C_n\$ in equation (4):

$$
C_n^{'} &lt; C_n + 0.1\,\% \; C_{n}\left ( \frac{T-T_0}{10} \right )
\;\;\;\;\;\;\;\;\;\;(4)
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\rightarrow
C_n^{'} &lt; C_n\, \left \{ 1 + \left ( \frac{1/10}{100} \right ) \left ( \frac{T-T_0}{10} \right ) \right \}
\;\;\;\;\;\;\;\;\;\;(5)
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\rightarrow
C_n^{'} &lt; C_n \left ( 1 + \frac{T-T_0}{10,000} \right ) \Bigg\rvert_{C_n=RHS\;of\;equation (3)}
\;\;\;\;\;\;\;\;\;\;(6)
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\rightarrow
C_n^{'} &lt; C_{n0} \left ( 1 + \frac{T-T_0}{20,000} \right ) \left ( 1 + \frac{T-T_0}{10,000} \right )
\;\;\;\;\;\;\;\;\;\;(7)
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\rightarrow C_n^{'} &lt; C_{n0} \left \{ 1 + \frac{3(T-T_0)}{20,000} + \frac{(T-T0)^2}{200,000,000} \right \}
\;\;\;\;\;\;\;(8)
$$

Various formulae in the amplifier module's data sheet have a "Sensitivity in mV/V" parameter; substitute \$C_n^{'}\$&mdash;i.e., the RHS of inequality (8)&mdash;for that sensitivity parameter.

:: DISCLAIMER :: Double-check these equations before using them in any product.



NOTES

1 At the top of page 17 of the amplifier module's data sheet there is a formula (above Example 1) where the word "sensitivity" refers to the load cell's sensitivity. So I'm assuming the "Effect of a 10 K-change in ambient temperature on sensitivity" spec on page 47 of the amplifier's data sheet also refers to the load cell's sensitivity.

2 The equations above are for the special case where the starting temperature \$T_0\$ and ending temperature \$T\$ are the same for both the load cell and the amplifier. I've provided a separate answer below for the more general case where the load cell's starting/ending temperatures can be different from the amplifier's starting/ending temperatures.