The design of adaptable drug delivery systems able to encapsulate and release drugs with different wettability has been attracting widespread interest. Additionally, many attempts have been made to tune hydrophobic/hydrophilic drug release kinetics over time, avoiding the so-called burst release. In this scenario, hydrogels resulting from the assembly of micellar structures showing a hydrophobic core and a hydrophilic shell could represent a promising alternative to design versatile drug vehicles. In this regard, this work aimed at designing new thermosensitive micellar hydrogels starting from a custom-made amphiphilic poly(ether urethane) (PEU). Specifically, a commercial triblock copolymer (Poloxamer® 407), selected to ensure the temperature-driven chain arrangement into micelles, was reacted with 1,6-diisocyanatohexane and 1,4-cyclohexanedimethanol. The successful PEU synthesis was proved by size-exclusion chromatography (w 50000 Da) and infrared spectroscopy. Subsequently, the wettability-driven drug arrangement within the micelle network as well as the influence of drug-loading on the resultant formulation thermosensitivity was investigated by selecting ibuprofen (IBU) and ibuprofen sodium salt (IBUSS) as hydrophobic and hydrophilic drugs, respectively. Specifically, growing drug amounts were loaded into PEU solutions, and the average hydrodynamic micelle diameters and the critical micellar temperatures (CMT) were measured. Systems containing IBU at the highest tested concentration (i.e., 20 mg/mL) showed a significantly higher micelle average diameter (58.2 ± 4.7 nm) and a remarkably lower CMT (8.9°C) with respect to both the control (40.1 ± 1.4 nm and 21.6°C) and IBUSS-loaded formulations (37.3 ± 2.1 nm and 22.4°C). Then, the influence of drug encapsulation on the temperature at which micelles begin to aggregate was rheologically assessed, showing that IBU-loading induced a decrease in this parameter (14.6, 8.7, and 13.7°C for virgin, IBU-loaded, and IBUSS-loaded hydrogel, respectively). Finally, IBU and IBUSS releasing mechanism was analysed using the Korsmayer–Peppas model (n value of 0.63 ± 0.007 and 0.89 ± 0.003 for IBU- and IBUSS-loaded gels, respectively). Thanks to their micellar organisation, the here-developed hydrogel platform allowed the encapsulation of a high number of molecules with different wettability. Additionally, these systems exhibited tunable payload-releasing time without burst release and open the way toward the engineering of smart systems for the sustained co-delivery of multiple drugs in a target tissue/organ.