This paper shows that a conductive domain which is subjected to heating from its bottom can be cooled with embedded microvascular cooling channels in it. The volume of the domain and the coolant are fixed. The actively cooled domain is mimicked from the human skin (which regulates temperature with microvascular blood vessels). The effect of the shape of cooling channels (sinusoidal or straight) and their locations in the direction perpendicular to the bottom surface on the peak and average temperatures are studied. In addition, the effect of pressure difference in between the inlet and outlet is varied. The pressure drop in the sinusoidal channel configurations is greater than the straight channel configurations for a fixed cooling channel volume. The peak and average temperatures are the smallest with straight cooling channels located at y = 0.7 mm. Furthermore, how the cooling channel configuration should change when the heat is generated throughout the volume is studied. The peak and average temperatures are smaller with straight channels than the sinusoidal ones when the pressure drop is less than 420 Pa, and they become smaller with sinusoidal channel configurations when the pressure drop is greater than 420 Pa. In addition, the peak and average temperatures are the smallest with sinusoidal channels for a fixed flow rate. Furthermore, the peak temperatures for multiple cooling channels is documented, and the multiple channel configurations promise to the smallest peak temperature for a fixed pressure drop value. This paper uncovers that there is no optimal cooling channel design for any condition, but there is one for specific objectives and conditions.