Here we present recent upgrades of the transportable strontium lattice clock at PTB. Its second-generation physics package was assembled, which includes a single-beam pyramid magneto-optical trap for two-stage laser cooling and an in-vacuum radiation shield for better thermal uniformity during the clock interrogation phase. The radiation shield can be cooled to cryogenic temperatures, where it supports fractional blackbody radiation shift uncertainties below 1E-18. Also the clock instability was improved by the use of a transportable clock laser with an instability of down to 1.6E-16.