diff --git a/sklearn/metrics/_pairwise_distances_reduction/_middle_term_computer.pyx.tp b/sklearn/metrics/_pairwise_distances_reduction/_middle_term_computer.pyx.tp
index 3363eb9524263..6b48ed519267b 100644
--- a/sklearn/metrics/_pairwise_distances_reduction/_middle_term_computer.pyx.tp
+++ b/sklearn/metrics/_pairwise_distances_reduction/_middle_term_computer.pyx.tp
@@ -368,8 +368,6 @@ cdef class DenseDenseMiddleTermComputer{{name_suffix}}(MiddleTermComputer{{name_
         ITYPE_t thread_num,
     ) nogil:
         cdef:
-            const {{INPUT_DTYPE_t}}[:, ::1] X_c = self.X[X_start:X_end, :]
-            const {{INPUT_DTYPE_t}}[:, ::1] Y_c = self.Y[Y_start:Y_end, :]
             DTYPE_t *dist_middle_terms = self.dist_middle_terms_chunks[thread_num].data()
 
             # Careful: LDA, LDB and LDC are given for F-ordered arrays
@@ -380,9 +378,9 @@ cdef class DenseDenseMiddleTermComputer{{name_suffix}}(MiddleTermComputer{{name_
             BLAS_Order order = RowMajor
             BLAS_Trans ta = NoTrans
             BLAS_Trans tb = Trans
-            ITYPE_t m = X_c.shape[0]
-            ITYPE_t n = Y_c.shape[0]
-            ITYPE_t K = X_c.shape[1]
+            ITYPE_t m = X_end - X_start
+            ITYPE_t n = Y_end - Y_start
+            ITYPE_t K = self.n_features
             DTYPE_t alpha = - 2.
 {{if upcast_to_float64}}
             DTYPE_t * A = self.X_c_upcast[thread_num].data()
@@ -391,15 +389,15 @@ cdef class DenseDenseMiddleTermComputer{{name_suffix}}(MiddleTermComputer{{name_
             # Casting for A and B to remove the const is needed because APIs exposed via
             # scipy.linalg.cython_blas aren't reflecting the arguments' const qualifier.
             # See: https://github.com/scipy/scipy/issues/14262
-            DTYPE_t * A = <DTYPE_t *> &X_c[0, 0]
-            DTYPE_t * B = <DTYPE_t *> &Y_c[0, 0]
+            DTYPE_t * A = <DTYPE_t *> &self.X[X_start, 0]
+            DTYPE_t * B = <DTYPE_t *> &self.Y[Y_start, 0]
 {{endif}}
-            ITYPE_t lda = X_c.shape[1]
-            ITYPE_t ldb = X_c.shape[1]
+            ITYPE_t lda = self.n_features
+            ITYPE_t ldb = self.n_features
             DTYPE_t beta = 0.
-            ITYPE_t ldc = Y_c.shape[0]
+            ITYPE_t ldc = Y_end - Y_start
 
-        # dist_middle_terms = `-2 * X_c @ Y_c.T`
+        # dist_middle_terms = `-2 * X[X_start:X_end] @ Y[Y_start:Y_end].T`
         _gemm(order, ta, tb, m, n, K, alpha, A, lda, B, ldb, beta, dist_middle_terms, ldc)
 
         return dist_middle_terms