Index: clang-tidy/performance/UnnecessaryValueParamCheck.cpp
===================================================================
--- clang-tidy/performance/UnnecessaryValueParamCheck.cpp
+++ clang-tidy/performance/UnnecessaryValueParamCheck.cpp
@@ -58,6 +58,18 @@
   return Matches.empty();
 }
 
+bool isExplicitTemplateSpecialization(const FunctionDecl &Function) {
+  if (const auto *SpecializationInfo = Function.getTemplateSpecializationInfo())
+    if (SpecializationInfo->getTemplateSpecializationKind() ==
+        TSK_ExplicitSpecialization)
+      return true;
+  if (const auto *Method = llvm::dyn_cast<CXXMethodDecl>(&Function))
+    if (Method->getTemplatedKind() == FunctionDecl::TK_MemberSpecialization &&
+        Method->getMemberSpecializationInfo()->isExplicitSpecialization())
+      return true;
+  return false;
+}
+
 } // namespace
 
 UnnecessaryValueParamCheck::UnnecessaryValueParamCheck(
@@ -133,9 +145,11 @@
   // 2. the function is virtual as it might break overrides
   // 3. the function is referenced outside of a call expression within the
   //    compilation unit as the signature change could introduce build errors.
+  // 4. the function is an explicit template specialization.
   const auto *Method = llvm::dyn_cast<CXXMethodDecl>(Function);
   if (Param->getLocStart().isMacroID() || (Method && Method->isVirtual()) ||
-      isReferencedOutsideOfCallExpr(*Function, *Result.Context))
+      isReferencedOutsideOfCallExpr(*Function, *Result.Context) ||
+      isExplicitTemplateSpecialization(*Function))
     return;
   for (const auto *FunctionDecl = Function; FunctionDecl != nullptr;
        FunctionDecl = FunctionDecl->getPreviousDecl()) {
Index: test/clang-tidy/performance-unnecessary-value-param.cpp
===================================================================
--- test/clang-tidy/performance-unnecessary-value-param.cpp
+++ test/clang-tidy/performance-unnecessary-value-param.cpp
@@ -348,3 +348,13 @@
   ExpensiveToCopyType E;
   NegativeUsingConstructor S(E);
 }
+
+template<typename T>
+void templateFunction(T) {
+}
+
+template<>
+void templateFunction<ExpensiveToCopyType>(ExpensiveToCopyType E) {
+  // CHECK-MESSAGES: [[@LINE-1]]:64: warning: the parameter 'E' is copied
+  E.constReference();
+}