> Heat pump have problems to reach high enough temperatures for most industrial heat applications.

They do if you start from ambient temperature, but they can be more effective if they are pumping heat out of the waste heat stream of a process. This requires different working fluids than lower temperature systems, though.

Most industrial heat energy is not consumed at very high temperature. IIRC, 2/3rds is at less than 300 C.

Electric resistance heating might also allow PV to dispense with auxiliary equipment, like inverters, so even if inefficient that might not matter as much. Heat also allows easy long duration storage at scale, even at rather high temperature, so resistive heating can be used with intermittently available cheap surplus power.

For example Haber process used for ammonia production, requires a temperature of at least 400 °C to be efficient. This process is accounting for 1–2% of global energy consumption, 3% of global carbon emissions, and 3% to 5% of natural gas consumption.

https://en.wikipedia.org/wiki/Haber_process

Electric resistance heating generated from PV will supply energy only for few hours each day.

Heating storage (also cold storage) in industrial applications is possible and is done, but in many cases you are limited by allowed temperature range of chemical/physical processes. For example you are limited on the lower side by melting temperature of material and on higher side by high temperature corrosion.

Cold storage for electric demand response https://www.enersponse.com/cold-storage

In cement industries models have been developed to flatten the grid's hourly demand curve by minimizing the industrial customer's hourly peak loads and maximizing the shifting of demand to off-peak periods.

https://www.sciencedirect.com/science/article/pii/S030626192...