Fouling is one of the most troublesome constraints in heat exchanger operation; it reduces heat duty and, as deposits grow, changes the exchanger dynamics, causing PID temperature controllers tuned for clean conditions to lose performance. This study examines whether the minimum temperature difference (ΔT_min) chosen at the design stage can limit this effect. A dynamic model of a shell-and-tube crude oil preheater (220 t/h) was implemented in MATLAB/Simulink R2025b, and closed-loop responses, control-quality indices and stability margins were compared for ΔT_min = 50 K and 10 K for clean and fouled (R_f = 0.00138 m²K/W) exchangers with Ziegler–Nichols PID settings. At ΔT_min = 50 K, fouling increased the set-point ISE by 75%, the settling time from 92 s to 231 s, and the overshoot from 57% to 65%, while reducing the phase margin from 25.7° to 15.8°; retuning was necessary and restored the phase margin to 27.8°. At ΔT_min = 10 K, the corresponding changes were much smaller (ISE increased by 27%, settling time increased from 107 s to 159 s, overshoot increased from 40% to 44%, and phase margin decreased by only 3.4°), so the original settings could be retained. Disturbance-rejection ISE grew 2.2-fold at 50 K versus 1.6-fold at 10 K. A lower ΔT_min is therefore a practical design guideline for reducing fouling-induced controller retuning.