diff --git a/docs/thermal-model.md b/docs/thermal-model.md
index 878c4df..0cd39d3 100644
--- a/docs/thermal-model.md
+++ b/docs/thermal-model.md
@@ -15,8 +15,14 @@ the trip happens.
 
 - **Parameters are fitted per install** (`wallmonitor/thermal.py`) from your
   own recorded charging ramps: the time constant τ and the steady-state rise
-  at 48 A. Defaults come from a telemetry-verified alert-40 event and are
-  replaced as sessions accumulate.
+  at 48 A. Defaults come from a telemetry-verified alert-40 event on one
+  install and are replaced as sessions accumulate. Once fitted, the
+  dashboard's model note says so when this install landed far (>30%) from
+  those priors: forecasts before the first fit were governed by numbers
+  that did not describe this charger, and an install with a τ well under
+  the default has a standing cost — the fitter judges a charge's window
+  against the default τ, so only charges of ~22 min or more at steady
+  current teach the model there.
 - **The charger is its own thermometer.** Idle, the handle sits ~1–2 °C above
   ambient (a calibrated, ambient-dependent offset — see
   `contrib/calibrate_idle_offset.py`), so ambient can be read without any
diff --git a/tests/test_wallmonitor.py b/tests/test_wallmonitor.py
index d3b6fe6..ba301a6 100644
--- a/tests/test_wallmonitor.py
+++ b/tests/test_wallmonitor.py
@@ -634,6 +634,21 @@ async def test_thermal_fit_slow_tau_install_still_fits(db):
         assert fit["rise_ref_c"] is not None and abs(fit["rise_ref_c"] - rise) < 3.0
 
 
+def test_thermal_params_report_prior_deviation():
+    # Unfitted: nothing to compare. Fitted near the defaults: reported but
+    # not notable. Fitted far off (a fast-tau, low-rise install): notable,
+    # with the sign the UI needs to warn that short charges won't fit.
+    assert thermal.ThermalParams().prior_deviation() is None
+    near = thermal.ThermalParams(tau_min=12.5, rise_ref_c=34.0, tau_fits=3, rise_fits=3)
+    dev = near.prior_deviation()
+    assert dev["notable"] is False and abs(dev["tau_frac"]) < 0.1
+    far = thermal.ThermalParams(tau_min=6.0, rise_ref_c=20.0, tau_fits=3, rise_fits=3)
+    dev = far.prior_deviation()
+    assert dev["notable"] is True and dev["tau_frac"] < -0.3 and dev["rise_frac"] < -0.3
+    assert dev["default_tau_min"] == thermal.DEFAULT_TAU_MIN
+    assert far.as_dict()["prior_deviation"] == dev
+
+
 async def test_thermal_fit_covers_late_charging_segments(db):
     # A session shaped like real overnight use: a plug-in burst too short to
     # fit, hours of connected idle, then distinct charging segments (vehicle
diff --git a/wallmonitor/static/app.js b/wallmonitor/static/app.js
index bd7a7ac..b59125f 100644
--- a/wallmonitor/static/app.js
+++ b/wallmonitor/static/app.js
@@ -1101,9 +1101,26 @@ async function viewLive(root) {
         (drift.off_current_n ? ` (${drift.off_current_n} session${drift.off_current_n === 1 ? "" : "s"} away from the usual ` +
         `~${fmtNum(drift.typical_current_a, 0)} A excluded from the comparison.)` : ""));
     }
+    // The defaults come from one verified install. Once this install has
+    // fits of its own, say plainly when they landed far from those priors:
+    // the forecast before the first fit was governed by numbers that did
+    // not describe this charger, and a fast tau has a standing cost — the
+    // fitter's identifiability gate is floored at the default tau, so short
+    // charges on such an install never teach the model.
+    const dev = model.prior_deviation;
+    let priorNote = "";
+    if (model.fitted && dev && dev.notable) {
+      const parts = [];
+      if (Math.abs(dev.tau_frac) > 0.3) parts.push(`τ ${fmtNum(model.tau_min, 1)} min vs the ${fmtNum(dev.default_tau_min, 0)} min default`);
+      if (Math.abs(dev.rise_frac) > 0.3) parts.push(`rise +${fmtNum(model.rise_ref_c, 0)} °C vs the +${fmtNum(dev.default_rise_ref_c, 0)} °C default`);
+      priorNote = ` This install differs from the built-in priors (${parts.join("; ")}) — forecasts before its first ` +
+        `fitted session were rough` +
+        (dev.tau_frac < -0.3 ? `, and with a τ this fast only charges of ≥ ${fmtNum(1.8 * dev.default_tau_min, 0)} min ` +
+          "at steady current teach the model." : ".");
+    }
     const modelNote = `Model: τ ≈ ${fmtNum(model.tau_min, 1)} min, +${fmtNum(model.rise_ref_c, 0)} °C at ${fmtNum(model.ref_current_a, 0)} A — ` +
-      (model.fitted ? `fitted from ${model.tau_fits} recorded session ramp${model.tau_fits === 1 ? "" : "s"}.`
-                : "defaults from the verified alert-40 event; refits automatically as sessions accumulate.") +
+      (model.fitted ? `fitted from ${model.tau_fits} recorded session ramp${model.tau_fits === 1 ? "" : "s"}.` + priorNote
+                : "defaults from one verified install, used until this charger has fits of its own; refits automatically as sessions accumulate.") +
       (drift && !drift.drifting && !drift.lead ? ` Heat rise stable across the last ${drift.recent_n + drift.baseline_n} fitted sessions` +
         `${drift.off_current_n ? ` (${drift.off_current_n} off-current session${drift.off_current_n === 1 ? "" : "s"} excluded)` : ""}.` : "");
     thermalCard.append(el("div", { class: "chart-card" },
diff --git a/wallmonitor/thermal.py b/wallmonitor/thermal.py
index 2e1df64..2f4e980 100644
--- a/wallmonitor/thermal.py
+++ b/wallmonitor/thermal.py
@@ -153,6 +153,32 @@ class ThermalParams:
     def fitted(self) -> bool:
         return self.tau_fits > 0 and self.rise_fits > 0
 
+    # How far a fitted value may sit from the default before the dashboard
+    # says the priors were a poor fit for this install. A heuristic, not a
+    # statistic: 30% is roughly where the default-driven forecast's plateau
+    # error exceeds the fit's own noise and early-session predictions were
+    # materially off.
+    PRIOR_DEVIATION_FRAC = 0.30
+
+    def prior_deviation(self) -> dict | None:
+        """How this install's fitted tau and rise compare to the defaults
+        that governed the forecast before its first fit landed — None until
+        fitted. The frontend renders it as an honesty note: the priors are
+        from one verified install, and a user whose charger differs should
+        know that early forecasts were rough and (for a fast tau) that short
+        charges no longer teach the model."""
+        if not self.fitted:
+            return None
+        tau_frac = self.tau_min / DEFAULT_TAU_MIN - 1.0
+        rise_frac = self.rise_ref_c / DEFAULT_RISE_REF_C - 1.0
+        return {
+            "default_tau_min": DEFAULT_TAU_MIN,
+            "default_rise_ref_c": DEFAULT_RISE_REF_C,
+            "tau_frac": round(tau_frac, 3),
+            "rise_frac": round(rise_frac, 3),
+            "notable": max(abs(tau_frac), abs(rise_frac)) > self.PRIOR_DEVIATION_FRAC,
+        }
+
     def as_dict(self) -> dict:
         """The `model` object served by /api/thermal and the SSE thermal
         frame — fitted values plus the fixed thresholds."""
@@ -168,6 +194,7 @@ def as_dict(self) -> dict:
             "rise_fits": self.rise_fits,
             "fit_rmse_c": round(self.fit_rmse_c, 3) if self.fit_rmse_c is not None else None,
             "fitted": self.fitted,
+            "prior_deviation": self.prior_deviation(),
         }