The most alarming blaze, near Baldomar in Catalonia, has already destroyed 500 hectares of forest but could spread to over 20,000, the government in the northwestern region said.
No-one has been evacuated yet but the Catalan authorities have cordoned off several residential areas as a precaution.
In Lerida province, where Baldomar is located, temperatures reached 41C on Thursday.
Spanish meteorologial office AEMET also forecast temperatures above 40C in Badajoz in the southwest and Zaragoza in the northeast.
Two other wildfires were raging in Catalonia on Thursday morning, in Lerida and Tarragona provinces, and had destroyed nearly 300 hectares, the Catalan authorities said.
Another was burning in the Sierra de la Culebra mountains in Zamora, central Spain.
In the northern province of Navarra, firefighters brought two forest fires under control during Wednesday night, regional emergency services said.
The six-day-old heatwave, exceptional in Spain for this time of year, has affected the entire country and is forecast to last until Saturday, AEMET said.
Spain recorded its hottest May since the start of the 21st century and has seen four extreme temperature episodes in less than a year.
In neighbouring Portugal, last month was the hottest May since 1931.
Heatwaves have become more prevalent due to climate change, scientists say.
As global temperatures rise over time, heatwaves are predicted to become more frequent and intense, and their impacts more widespread.
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