Correction formula for alcoholmeter
I have had the same question recently. And there is no simple answer. Tables (like ones from International critical tables of numerical data, physics, chemistry and technology or this) are still the 1st hand source. Formulas used are just approximating this data. Check formula here on page 8 (to get the temperature-corrected ABV you have to invert it by solving non-linear function). Alternatively check this recent study. To convert between ABV (alcohol by volume, %) and density (specific gravity SG, g/cm3) you may use this approximation:

$$\mathrm{SG} = -0.002\cdot\mathrm{ABV} + 1.0012$$

PS. There is an unconfirmed formula at vinolab:


  The hydrometer temperature correction for SG is performed with this expression:
  
  $$\text{corrected-reading} = r \times \frac{(1.00130346 - (0.000134722124 \cdot t) + (0.00000204052596 \cdot t^2)\ - (0.00000000232820948 \cdot t^3))} {(1.00130346 - (0.000134722124 \cdot c) + (0.00000204052596 \cdot c^2)\ - (0.00000000232820948 \cdot c^3))}$$
  
  where: $r$ = reading and $c$ = calibration temperature. This expression is based on °F, so the temperatures are first converted.


With some sample values it gave me results close to the table' ones (I have converted ABV to SG, amended as per temperature and formula above and finally converted back to ABV).