You may try polyvinylcaprolactam with high molecular weight, having LCST = 32C. Strictly it is not a biopolymer, but its structure is similar to PVP, widely used in medicine.
You might be interested on poloxamers which can be mixed to tune the phase transition temperature, see e.g. DOI: 10.1002/adhm.201600055. Also these are not biobased but regularly used for bioapplications.
You may consider methylcellulose-based hydrogels, whose LCST can be tuned by adjusting the polymer's concentration and the saline solution used to prepare the hydrogel (DOI 10.1007/s10856-016-5703-8). In our lab we successfully used these hydrogles for 3d printing and bioprinting applications (DOI 10.3390/ma11040579, DOI 10.1016/j.bprint.2018.e00024)