Air carrier Captain flying an EMB-145 aircraft reported an anti-ice system malfunction inflight.

Narrative

After departure from ZZZ1 flight began receiving vectors due to flow into ZZZ. Flight crew monitored fuel load and eventually declared minimum fuel while with Center. While enroute; aircraft encountered icing conditions. Shortly after the Bleed 1 Low Temp EICAS message appeared. Following the QRH procedures eliminated the message for a time; but the message then returned while the aircraft was already at a high power setting and a fast speed and no more power was available to raise the bleed temperature. The message cleared when the aircraft exited ice. During the descent into ZZZ while passing through 10;000 ft. the aircraft again encountered icing conditions. This time the message wing stab A/I (anti-ice) fail message displayed. The bottom of the cloud layer was just below us and an increased power setting allowed the icing system to operate. The Captain opted to increase the power in the descent to keep the bleeds up until below the clouds and out of icing conditions. The Captain was aware that this would cause the aircraft to exceed the 250 kt. speed limit below 10;000 ft. but decided it was a safer option to escape the ice. The Captain informed ATC and [received priority]. When clear of icing conditions the Captain canceled the [priority] and the flight resumed without further issues. Upon landing Captain notified the controlling Dispatcher and spoke with Maintenance Control and made a maintenance write-up in the aircraft log.Root Cause - The bleeds were too low temperature at even relatively high power settings. The aircraft icing system; specifically the Wing/Stab anti ice system failed to operate at power settings required to fly under 250 kts. even when level.