Hyperbranched polyamidoamine (HPAMAM) polymers, chemically analogous to the commercially available PAMAM dendrimer, were modified with isobutyric anhydride to result in isobutyramide (IBAm) terminated HPAMAMs (HPAMAM-IBAm). The aqueous solutions of HPAMAM-IBAm polymers had the lower critical solution temperature (LCST). The lower molecular-weight HPAMAM-IBAm exhibited higher LCST and the LCST difference was around $18^{circ}C$ for one pseudo-generation variation. Further, the hyperbranched thermoresponsive polymers exhibited much lower LCSTs than the corresponding dendrimers with similar molecular weight. The LCST of HPAMAM-IBAm was pH sensitive. At pH below 10, the LCST increased significantly upon decreasing the pH, whereas, at pH above 10, the LCST decreased slowly with an increasing pH value. Nine sodium salts were used to measure the anion effect on the LCST of HPAMAM-IBAm. It was found that the LCST could also be modulated up or down in a broad range by simply adding a small amount of different kinds of inorganic anions. The specific ranking of inorganic anions in salting-out HPAMAM4-IBAm polymer was in accordance with the well-known Hofmeister series.