What GH is it? "Generic" or pharmaceutical? If it's pharmaceutical I can find documentation for you on that.
IIRC, it does not need to be refrigerated prior to being reconstituted - just kept below a certain temperature.
Edit:
From an old post of mine on another forum:
Saizen® 5 mg and 8.8 mg vials reconstituted with the Bacteriostatic Water for Injection, USP (0.9% Benzyl Alcohol) provided should be stored under refrigeration (36°–46°F/2°–8°C) for up to 14 days.
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All Norditropin® products must be refrigerated prior to first use. Do not freeze. After initial use, Norditropin® pens can either be stored outside of the refrigerator (up to 77°F) for use within 3 weeks, or in the refrigerator (between 36°F and 46°F) for use within 4 weeks.
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The reconstituted solution should be stored under refrigeration (between 36°F and 46°F) for up to 14 days. Avoid freezing reconstituted vials of Serostim®.
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Between uses, store your GENOTROPIN PEN 5 in the refrigerator at 36°F to 46°F (2 °C to 8°C) in its protective case.
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Humatrope must be kept refrigerated (36° to 46°F [2° to 8°C]) before and after it is mixed.
Source