First of All, there is no such exemption is available for the Cold Storage Service w.e.f. 01.07.2012 as there is no exepmtion is granted in Negative List and in Mega Exepmtion Notification No. 25/2012 - ST Dated : 20/06/2012 hence Service Tax is applicable for the Storage Service.
Further, IIf you handling Charges are composite then there will not be any separate effect of Transportation. But if you are raising the Separate Bill for Transportation, then If your receiving Party is liable for Service Tax payment i.e. as under as per Notification 15/2012 - ST 20/06/2012
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(ii) provided or agreed to be provided by a goods transport agency in respect of transportation of goods by road, where the consignor or the consignee is,—
(a) any factory registered under or governed by the Factories Act, 1948 (63 of 1948);
(b) any society registered under the Societies Registration Act, 1860 (21 of 1860) or under any other law for the time being in force in any part of India;
(c) any co-operative society established by or under any law;
(d) any dealer of excisable goods, who is registered under the Central Excise Act, 1944 (1 of 1944) or the rules made thereunder;
(e) any body corporate established, by or under any law; or
(f) any partnership firm whether registered or not under any law including association of persons;"