diff --git a/systems/Frontier/schur2d_env.job b/systems/Frontier/schur2d_env.job
index fd974576a..7556ee544 100644
--- a/systems/Frontier/schur2d_env.job
+++ b/systems/Frontier/schur2d_env.job
@@ -4,7 +4,7 @@
 #SBATCH --ntasks-per-node=8
 #SBATCH --cpus-per-task=7
 #SBATCH --gpus-per-node=8
-#SBATCH --time=0:40:00
+#SBATCH --time=0:50:00
 #SBATCH --account=phy157_dwf
 #SBATCH --gpu-bind=none
 #SBATCH --exclusive
@@ -70,7 +70,7 @@ run_cell () {
   fname=log.env.$name
   env "$@" srun -N36 -n288 --kill-on-bad-exit=1 ./select_gpu $BIN --mpi ${MPI_GEOM} --grid $vol $OPTS1 > $fname 2>&1
   echo "  exit $?"; sleep 30
-  grep -h "PROBE banner\|device ballast\|PROBE leaf\|BIG LEAVES\|gemm min/max\|invert\|certificate" $fname \
+  grep -h "PROBE banner\|device ballast\|pre-heat\|PROBE leaf\|BIG LEAVES\|gemm min/max\|invert\|certificate" $fname \
     | sed 's/^Grid : Message : [0-9.]* s : //' | cut -c1-170
 }
 
@@ -81,6 +81,11 @@ run_cell   E3_omp7           OMP_NUM_THREADS=7
 run_cell   E4_omp7_ballast   OMP_NUM_THREADS=7 S2D_BALLAST_GB=10.6                                            # + the example's device residency
 run_cell   E5_omp1_ballast   OMP_NUM_THREADS=1 S2D_BALLAST_GB=10.6                                            # ballast alone
 run_cell   E6_omp1_again     OMP_NUM_THREADS=1                                                                 # repeat E1: the noise floor
+# E1-E4 (2026-08-27): 24.5 (first cell, cold) / 21.2 / 21.3 / 21.35 s -- thread level, OMP, residency all cleared.
+# Remaining difference from the example (26.5-27.6 s, local kernels 20-40% slower, wires equal): the example
+# inverts after ~100 s of full load on every GCD.  Pre-heat reproduces that; "last zgemm" TF/s vs 23.7 is the tell.
+run_cell   E7_omp7_preheat   OMP_NUM_THREADS=7 S2D_PREHEAT_S=100                                              # sustained load before the invert
+run_cell   E8_omp7_preheat_ballast OMP_NUM_THREADS=7 S2D_PREHEAT_S=100 S2D_BALLAST_GB=10.6                    # the example's full state
 
 echo "========================================================="
 echo "summary"
diff --git a/tests/debug/Test_schur2d_scale.cc b/tests/debug/Test_schur2d_scale.cc
index 609e76c88..bbe88bfb5 100644
--- a/tests/debug/Test_schur2d_scale.cc
+++ b/tests/debug/Test_schur2d_scale.cc
@@ -139,6 +139,31 @@ int main(int argc, char **argv)
   BlockCyclicMatrix A0(grid,N,nb,Pr,Pc);
   BlockCyclicSchurInverse RSI2;
 
+  // Pre-heat: drive the GCD with back-to-back zgemm for S2D_PREHEAT_S seconds
+  // before the invert.  The example calls the inverse after ~100 s of full
+  // load on all 288 GCDs and its LOCAL kernels run 20-40% slower than the
+  // idle-start harness (GEMM 3.1 vs 2.5 s, leaf 0.76 vs 0.24 s) with the
+  // wires unchanged; thread level / OMP / residency (E1-E5) did not reproduce
+  // that.  If sustained load does, it is clock/power management, not code.
+  if ( getenv("S2D_PREHEAT_S") ) {
+    double secs = atof(getenv("S2D_PREHEAT_S"));
+    const int64_t W = 4320;
+    deviceVector<ComplexD> M((uint64_t)W*W), C((uint64_t)W*W);
+    { ComplexD *m = &M[0]; accelerator_for(idx,(uint64_t)W*W,1,{ m[idx] = ComplexD(1.0e-3*(idx%97),1.0e-3*(idx%89)); }); accelerator_barrier(); }
+    deviceVector<ComplexD*> ap(1),bp(1),cp(1); std::vector<ComplexD*> ptr(1);
+    ptr[0]=&M[0]; acceleratorCopyToDevice(&ptr[0],&ap[0],sizeof(ComplexD*)); acceleratorCopyToDevice(&ptr[0],&bp[0],sizeof(ComplexD*));
+    ptr[0]=&C[0]; acceleratorCopyToDevice(&ptr[0],&cp[0],sizeof(ComplexD*));
+    double t0=usecond(); int n=0; double tlast=0;
+    while ( (usecond()-t0)/1.0e6 < secs ) {
+      double t1=usecond();
+      RSI2.SUMMA.BLAS.gemmBatched(GridBLAS_OP_N,GridBLAS_OP_N,(int)W,(int)W,(int)W,ComplexD(1.0,0.0),ap,(int)W,bp,(int)W,ComplexD(0.0,0.0),cp,(int)W);
+      RSI2.SUMMA.BLAS.synchronise(); tlast=usecond()-t1; n++;
+    }
+    double tfirst = 0; (void)tfirst;
+    std::cout << GridLogMessage << "Test_schur2d_scale: pre-heat " << (usecond()-t0)/1.0e6 << " s, " << n << " zgemm W=" << W
+              << ", last zgemm " << tlast/1.0e6 << " s (" << 8.0*W*W*W/tlast/1.0e6 << " TF/s; idle-start rate 23.7)" << std::endl;
+  }
+
   // Device ballast: Lattice fields written on the accelerator so they sit in
   // the MemoryManager's device LRU exactly as the example's fine-grid state does.
   typedef Lattice<iVector<iVector<vComplexD,Nc>,Ns> > BallastField;