The limited cooling capacity of cold plates employing conventional channel designs represents a key obstacle in thermal management systems. The persistent growth of the thermal boundary layer and the uneven distribution of flow across the channels are the principal challenges encountered in this context. To overcome these challenges, this study aims to analyse a modified cold plate of obstructed variable-width channels that can improve the hydrothermal performance and temperature uniformity. Different shapes of pin fins and grooves with variable sizes that match the width of the variable-width channels are proposed. Specifically, four types of pin fins–grooves were used: ellipse, drop, rhombus and trapezoid. The traditional cold plate served as a basis for evaluating the performance of new designs of cold plates. In addition to the traditional cold plate, the four proposed designs of cold plates were manufactured from copper. Experiments were conducted with water as a working fluid under a laminar flow for a flow rate range of 0.004–0.04 kg/s and a discharge C-rate range of 1C–2C. Results indicated that the use of variable-width channels with all shapes of fins–grooves effectively contributed to improving the heat dissipation of the cold plate, accompanied with an increase in hydraulic pumping power. At the highest flow rate, the best improvement percentage in the Nusselt number of 82.5% was achieved when trapezoidal pin fins–grooves were used; by contrast, the lowest pumping power increasing percentage of 33.2% was obtained when elliptical pin fins–grooves were adopted. The best hydraulic/thermal performance was achieved when trapezoidal pin fins were utilised, with the highest figure of merit of 1.685.